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 …

In this paper we prove that for every $ s\geq 2$ and every graph $ H $ the following holds.
Let $ G $ be a graph with average degree $\Omega_H (s^{C| H|^ 2}) $, for some absolute …

If a graph has no large balanced bicliques, but has large minimum degree, then what can
we say about its induced subgraphs? This question motivates the study of degree …

Let G and H be two vertex disjoint graphs. The union G∪ H is the graph with V (G∪ H)= V
(G)∪(H) and E (G∪ H)= E (G)∪ E (H). The join G+ H is the graph with V (G+ H)= V (G)∪ V …

Given a set H of graphs, let f H⋆: N> 0→ N> 0 be the optimal χ-binding function of the class
of H-free graphs, that is, f H⋆(ω)= max {χ (G): G is H-free, ω (G)= ω}. In this paper, we …

Given a positive integer t, let P t and K t respectively denote the chordless path and the
complete graph on t vertices. For a graph G, let χ (G) and ω (G) respectively denote the …

Abstract The Erdős-Hajnal conjecture is one of the most classical and well-known problems
in extremal and structural combinatorics dating back to 1977. It asserts that in stark contrast …

In this paper, we give an optimal χ-binding function for the class of (P 7, C 4, C 5)-free
graphs. We show that every (P 7, C 4, C 5)-free graph G has χ (G)≤⌈ 11 9 ω (G)⌉. To prove …

We use $ P_t $ and $ C_t $ to denote a path and a cycle on $ t $ vertices, respectively. A
{\em bull} is a graph consisting of a triangle with two disjoint pendant edges, a {\em hammer} …

A hereditary class of graphs is χ-bounded if there is a function f such that every graph G in
the class has chromatic number at most f (ω (G)), where ω (G) is the clique number of G; and …