A class of graphs is hereditary if it is closed under isomorphism and induced subgraphs. A class G of graphs is χ-bounded if there exists a function f : N → N such that for all graphs G ∈ G, and all… (More)

A class G of graphs is said to be χ-bounded if there is a function f : N → R such that for all G ∈ G and all induced subgraphs H of G, χ(H) ≤ f(ω(H)). In this paper, we show that if G is a χ-bounded… (More)

We prove that a graph G contains no induced four-edge path and no induced complement of a four-edge path if and only if G is obtained from five-cycles and split graphs by repeatedly applying the… (More)

Remarks: • If (A,B,C) is a cut-partition of a graph G, then C is a cutset of G. • Every cutset of a graph G gives rise to at least one cut-partition of G. Definition. A graph is k-connected if it has… (More)

An equivalence is a binary relational system A = (A, ρA) where ρA is an equivalence relation on A. A simple expansion of an equivalence is a system of the form (Aa1 an) were A is an equivalence and… (More)

We prove that a graph G contains no induced 5-vertex path and no induced complement of a 5-vertex path if and only if G is obtained from 5-cycles and split graphs by repeatedly applying the following… (More)

The bull is a graph consisting of a triangle and two vertex-disjoint pendant edges. A graph is called bull-free if no induced subgraph of it is a bull. A graph G is perfect if for every induced… (More)