When dealing with special graph classes and algorithmic problems on them, a main source
is the classical book of Golumbic, Algorithmic Graph Theory and Perfect Graphs [454]. The …

A graph G with clique number ω (G) ω (G) and chromatic number χ (G) χ (G) is perfect if χ
(H)= ω (H) χ (H)= ω (H) for every induced subgraph H of G. A family GG of graphs is called χ …

There is a great variety of colouring concepts and results in the literature. Here our focus is
to survey results on vertex colourings of graphs defined in terms of forbidden induced …

In this paper, we study the chromatic number of 2 K 2-free graphs. We show linear χ-binding
functions for several subclasses of 2 K 2-free graphs, namely (2 K 2, H)-free graphs where …

Abstract (EN) For a set of graphs H, we call a graph G H-free if GS is non-isomorphic to H for
each S⊆ V (G) and each H∈ H. Let f_H^*∶ N_ (> 0)↦ N_ (> 0) be the optimal χ-binding …

Let G be a graph. We say that G is perfectly divisible if for each induced subgraph H of G, V
(H) can be partitioned into A and B such that H [A] is perfect and ω (H [B])< ω (H). We use P t …

For a graph G, let χ (G) and ω (G), respectively, denote the chromatic number and clique
number of G. We give an explicit structural description of (P 5, gem)‐free graphs, and show …

The class of 2K2-free graphs includes several interesting subclasses such as split, pseudo-
split, threshold graphs, complements to chordal, interval or trivially perfect graphs. The …

Finding families that admit a linear $\chi $-binding function is a problem that has interested
researchers for a long time. Recently, the question of finding linear subfamilies of $2 K_2 …

For a graph GG, let χ (G) χ(G) (ω (G) ω(G)) denote its chromatic (clique) number. AP 2+ P 3
P_2+P_3 is the graph obtained by taking the disjoint union of a two‐vertex path P 2 P_2 and …