assumed
Is axiomatic knowledge from the viewpoint of HOPS website.
- complete upper bounds connected by a constant – by definition
- complete upper bounds cluster by a constant – by definition
- tree upper bounds connected by a constant – by definition
- tree upper bounds forest by a constant – by definition
- path upper bounds connected by a constant – by definition
- path upper bounds linear forest by a constant – by definition
- star upper bounds connected by a constant – by definition
- star upper bounds stars by a constant – by definition
- cycle upper bounds connected by a constant – by definition
- cycle upper bounds cycles by a constant – by definition
- graph class chordal is included in graph class perfect
- graph class perfect is not included in graph class chordal
- graph class cograph is included in graph class perfect
- graph class perfect is not included in graph class cograph
- graph class bipartite is included in graph class perfect
- graph class perfect is not included in graph class bipartite
- graph class cluster is included in graph class interval
- graph class interval is not included in graph class cluster
- graph class cluster is included in graph class cograph
- graph class cograph is not included in graph class cluster
- graph class linear forest is included in graph class interval
- graph class interval is not included in graph class linear forest
- graph class stars is included in graph class interval
- graph class interval is not included in graph class stars
- graph class interval is included in graph class chordal
- graph class chordal is not included in graph class interval
- graph class co-cluster is included in graph class cograph
- graph class cograph is not included in graph class co-cluster
- graph class forest is included in graph class bipartite
- graph class bipartite is not included in graph class forest
- graph class outerplanar is included in graph class planar
- graph class planar is not included in graph class outerplanar
- graph class complete is included in graph class co-cluster
- graph class co-cluster is not included in graph class complete
- graph class block is included in graph class chordal
- graph class chordal is not included in graph class block
- graph class cluster is included in graph class block
- graph class block is not included in graph class cluster
- graph class linear forest is included in graph class forest
- graph class forest is not included in graph class linear forest
- graph class disjoint cycles is included in graph class outerplanar
- graph class outerplanar is not included in graph class disjoint cycles
- graph class forest is included in graph class disjoint cycles
- graph class disjoint cycles is not included in graph class forest
- graph class forest is included in graph class block
- graph class block is not included in graph class forest
- graph class edgeless is included in graph class linear forest
- graph class linear forest is not included in graph class edgeless
- graph class stars is included in graph class forest
- graph class forest is not included in graph class stars
- graph class edgeless is included in graph class stars
- graph class stars is not included in graph class edgeless
- graph class edgeless is included in graph class co-cluster
- graph class co-cluster is not included in graph class edgeless
- graph class grid is included in graph class planar
- graph class planar is not included in graph class grid
- graph class grid is included in graph class bipartite
- graph class bipartite is not included in graph class grid
- graph class cycles is included in graph class disjoint cycles
- graph class disjoint cycles is not included in graph class cycles
- graph class grid is included in graph class connected
- graph class connected is not included in graph class grid
- graph class edgeless is included in graph class cluster
- graph class cluster is not included in graph class edgeless
- graph class star is included in graph class tree
- graph class tree is not included in graph class star
- graph class path is included in graph class tree
- graph class tree is not included in graph class path
- graph class path is included in graph class grid
- graph class grid is not included in graph class path
- pathwidth+maxdegree upper bounds pathwidth by a linear function – by definition
- pathwidth+maxdegree upper bounds maximum degree by a linear function – by definition
- degree treewidth upper bounds maximum degree by a linear function – by definition
- degree treewidth upper bounds treewidth by a linear function – by definition
- complete upper bounds distance to complete by a constant – by definition
- co-cluster upper bounds distance to co-cluster by a constant – by definition
- cograph upper bounds distance to cograph by a constant – by definition
- cluster upper bounds distance to cluster by a constant – by definition
- linear forest upper bounds distance to linear forest by a constant – by definition
- outerplanar upper bounds distance to outerplanar by a constant – by definition
- block upper bounds distance to block by a constant – by definition
- edgeless upper bounds distance to edgeless by a constant – by definition
- forest upper bounds distance to forest by a constant – by definition
- bipartite upper bounds distance to bipartite by a constant – by definition
- planar upper bounds distance to planar by a constant – by definition
- chordal upper bounds distance to chordal by a constant – by definition
- stars upper bounds distance to stars by a constant – by definition
- perfect upper bounds distance to perfect by a constant – by definition
- interval upper bounds distance to interval by a constant – by definition
- maximum degree upper bounds distance to maximum degree by a linear function – by definition
- bounded components upper bounds distance to bounded components by a linear function – by definition
- disconnected upper bounds distance to disconnected by a constant – by definition
- diameter+max degree upper bounds diameter by a linear function – by definition
- diameter+max degree upper bounds maximum degree by a linear function – by definition
- vertex connectivity is equivalent to distance to disconnected – By definition
- distance to disconnected is equivalent to vertex connectivity – By definition
- vertex integrity upper bounds distance to bounded components by a linear function – By definition
- distance to bounded components upper bounds vertex integrity by a linear function – By definition
- bandwidth upper bounds topological bandwidth by a linear function – By definition
- twin-cover number upper bounds distance to cluster by a linear function – By definition
- vertex cover upper bounds twin-cover number by a linear function – By definition
- average degree upper bounds minimum degree by a linear function – By definition
- diameter upper bounds average distance by a linear function – By definition
- maximum matching upper bounds maximum induced matching by a linear function – By definition
- distance to interval upper bounds boxicity by a linear function – By definition
- bisection bandwidth upper bounds edge connectivity by a linear function – By definition
- edgeless upper bounds bounded components by a constant – By definition
- grid upper bounds maximum degree by a constant – By definition
- bounded components upper bounds maximum degree by a linear function – By definition
- linear forest upper bounds maximum degree by a constant – By definition
- cycles upper bounds maximum degree by a constant – By definition
- diameter upper bounds treelength by a linear function – By definition
- graph class edgeless is not included in graph class connected – By definition
- graph class edgeless is not included in graph class cycles – By definition
- diameter+max degree upper bounds bounded components by an exponential function – folklore
- maximum independent set upper bounds bipartite number by a linear function – folklore
- bounded minimum degree does not imply bounded average degree – folklore
- size upper bounds vertex cover by a linear function – By definition
- size upper bounds maximum leaf number by a linear function – By definition
- size upper bounds distance to complete by a linear function – By definition
- size upper bounds bounded components by a linear function – By definition
- graphs with bounded size are not included in graph class planar – By definition
- graphs with bounded size are not included in graph class perfect – By definition
- graphs with bounded size are not included in graph class connected – By definition
- maximum matching on bipartite graphs upper bounds bipartite by a linear function – by definition
- maximum matching on bipartite graphs upper bounds maximum matching by a linear function – by definition
- connected is equivalent to connected – assumed
- bipartite is equivalent to bipartite – assumed
- block is equivalent to block – assumed
- chordal is equivalent to chordal – assumed
- cluster is equivalent to cluster – assumed
- co-cluster is equivalent to co-cluster – assumed
- cograph is equivalent to cograph – assumed
- complete is equivalent to complete – assumed
- forest is equivalent to forest – assumed
- tree is equivalent to tree – assumed
- interval is equivalent to interval – assumed
- edgeless is equivalent to edgeless – assumed
- linear forest is equivalent to linear forest – assumed
- path is equivalent to path – assumed
- outerplanar is equivalent to outerplanar – assumed
- perfect is equivalent to perfect – assumed
- planar is equivalent to planar – assumed
- stars is equivalent to stars – assumed
- star is equivalent to star – assumed
- cycles is equivalent to cycles – assumed
- cycle is equivalent to cycle – assumed
- disjoint cycles is equivalent to disjoint cycles – assumed
- grid is equivalent to grid – assumed
- disconnected is equivalent to disconnected – assumed
- size is equivalent to size – assumed
- vertex cover is equivalent to vertex cover – assumed
- maximum matching is equivalent to maximum matching – assumed
- vertex integrity is equivalent to vertex integrity – assumed
- treedepth is equivalent to treedepth – assumed
- clique cover number is equivalent to clique cover number – assumed
- maximum independent set is equivalent to maximum independent set – assumed
- domination number is equivalent to domination number – assumed
- twin-cover number is equivalent to twin-cover number – assumed
- edge clique cover number is equivalent to edge clique cover number – assumed
- neighborhood diversity is equivalent to neighborhood diversity – assumed
- modular-width is equivalent to modular-width – assumed
- iterated type partitions is equivalent to iterated type partitions – assumed
- maximum leaf number is equivalent to maximum leaf number – assumed
- feedback edge set is equivalent to feedback edge set – assumed
- genus is equivalent to genus – assumed
- cutwidth is equivalent to cutwidth – assumed
- carving-width is equivalent to carving-width – assumed
- bandwidth is equivalent to bandwidth – assumed
- topological bandwidth is equivalent to topological bandwidth – assumed
- bisection bandwidth is equivalent to bisection bandwidth – assumed
- maximum degree is equivalent to maximum degree – assumed
- c-closure is equivalent to c-closure – assumed
- feedback vertex set is equivalent to feedback vertex set – assumed
- shrub-depth is equivalent to shrub-depth – assumed
- linear clique-width is equivalent to linear clique-width – assumed
- pathwidth is equivalent to pathwidth – assumed
- pathwidth+maxdegree is equivalent to pathwidth+maxdegree – assumed
- d-path-free is equivalent to d-path-free – assumed
- treewidth is equivalent to treewidth – assumed
- mm-width is equivalent to mm-width – assumed
- degree treewidth is equivalent to degree treewidth – assumed
- contraction complexity is equivalent to contraction complexity – assumed
- branch width is equivalent to branch width – assumed
- clique-width is equivalent to clique-width – assumed
- clique-tree-width is equivalent to clique-tree-width – assumed
- rank-width is equivalent to rank-width – assumed
- linear rank-width is equivalent to linear rank-width – assumed
- boolean width is equivalent to boolean width – assumed
- inf-flip-width is equivalent to inf-flip-width – assumed
- twin-width is equivalent to twin-width – assumed
- radius-r flip-width is equivalent to radius-r flip-width – assumed
- book thickness is equivalent to book thickness – assumed
- h-index is equivalent to h-index – assumed
- acyclic chromatic number is equivalent to acyclic chromatic number – assumed
- odd cycle transversal is equivalent to odd cycle transversal – assumed
- degeneracy is equivalent to degeneracy – assumed
- chromatic number is equivalent to chromatic number – assumed
- average degree is equivalent to average degree – assumed
- minimum degree is equivalent to minimum degree – assumed
- maximum clique is equivalent to maximum clique – assumed
- edge connectivity is equivalent to edge connectivity – assumed
- vertex connectivity is equivalent to vertex connectivity – assumed
- boxicity is equivalent to boxicity – assumed
- chordality is equivalent to chordality – assumed
- maximum induced matching is equivalent to maximum induced matching – assumed
- diameter is equivalent to diameter – assumed
- average distance is equivalent to average distance – assumed
- girth is equivalent to girth – assumed
- domatic number is equivalent to domatic number – assumed
- arboricity is equivalent to arboricity – assumed
- mim-width is equivalent to mim-width – assumed
- sim-width is equivalent to sim-width – assumed
- module-width is equivalent to module-width – assumed
- tree-independence number is equivalent to tree-independence number – assumed
- NLC-width is equivalent to NLC-width – assumed
- NLCT-width is equivalent to NLCT-width – assumed
- linear NLC-width is equivalent to linear NLC-width – assumed
- bounded components is equivalent to bounded components – assumed
- distance to complete is equivalent to distance to complete – assumed
- distance to co-cluster is equivalent to distance to co-cluster – assumed
- distance to cograph is equivalent to distance to cograph – assumed
- distance to cluster is equivalent to distance to cluster – assumed
- distance to linear forest is equivalent to distance to linear forest – assumed
- distance to outerplanar is equivalent to distance to outerplanar – assumed
- distance to block is equivalent to distance to block – assumed
- distance to edgeless is equivalent to distance to edgeless – assumed
- distance to forest is equivalent to distance to forest – assumed
- distance to bipartite is equivalent to distance to bipartite – assumed
- distance to planar is equivalent to distance to planar – assumed
- distance to chordal is equivalent to distance to chordal – assumed
- distance to stars is equivalent to distance to stars – assumed
- distance to perfect is equivalent to distance to perfect – assumed
- distance to interval is equivalent to distance to interval – assumed
- distance to maximum degree is equivalent to distance to maximum degree – assumed
- distance to bounded components is equivalent to distance to bounded components – assumed
- distance to disconnected is equivalent to distance to disconnected – assumed
- bipartite number is equivalent to bipartite number – assumed
- treelength is equivalent to treelength – assumed
- diameter+max degree is equivalent to diameter+max degree – assumed
- maximum matching on bipartite graphs is equivalent to maximum matching on bipartite graphs – assumed