Diestel2017

@book{Diestel2017,
author = {Reinhard Diestel},
edition = {5th},
isbn = {3662536218},
publisher = {Springer Publishing Company, Incorporated},
title = {Graph Theory},
year = {2017},
}

• page 3 : complete – If all the vertices of $G$ are pairwise adjacent, then $G$ is \emph{complete}.
• page 5 : edgeless – A vertex of degree $0$ is \emph{isolated}.
• page 13 : forest – An acyclic graph, one not containing any cycles, is called a \emph{forest}.
• page 17 : bipartite – Instead of `2-partite’ one usually says bipartite.
• page 89 : planar – When we draw a graph on a piece of paper, we naturally try to do this as transparently as possible. One obvious way to limit the mess created by all the lines is to avoid intersections. … Graphs drawn in this way are called \emph{plane graphs}; abstract graphs that can be drawn in this way are called \emph{planar}.
• page 115 : outerplanar – A graph is called outerplanar if it has a drawing in which every vertex lies on the boundary of the outer face.
• page 135 : chordal – … a graph is chordal (or triangulated) if each of its cycles of length at least $4$ has a chord, i.e. if it contains no induced cycles other than triangles.
• page 135 : perfect – A graph is called perfect if every induced subgraph $H \subseteq G$ has chromatic number $\chi(H)=\omega(H)$, i.e. if the trivial lower bound of $\omega(H)$ colours always suffices to colour the vertices of $H$.
• page 145 : interval – A graph $G$ is called an \emph{interval graph} if there exists a set ${ I_v \mid v \in V(G) }$ of real intervals such that $I_u \cap I_v \ne \emptyset$ if and only if $uv \in E(G)$.