Given two graphs H 1 and H 2, a graph G is (H 1, H 2)-free if it contains no induced
subgraph isomorphic to H 1 or H 2. AP t is the path on t vertices. A chair is a P 4 with an …

Given a hereditary class of graphs G, a function f: N→ N such that f (1)= 1 and f (x)≥ x, for all
x∈ N is a χ-binding function for G if χ (G)≤ f (ω (G)), for each G∈ G. The class G is called χ …

Given two graphs H 1 and H 2, a graph is (H 1, H 2)-free if it contains no induced subgraph
isomorphic to H 1 nor H 2. A dart is the graph obtained from a diamond by adding a new …

A graph is k-vertex-critical if χ (G)= k but χ (Gv)< k for all v∈ V (G). We construct new infinite
families of k-vertex-critical (P 5, C 5)-free graphs for all k≥ 6. Our construction generalises …

Given two graphs H 1 and H 2, a graph is (H 1, H 2)-free if it contains no induced subgraph
isomorphic to H 1 or H 2. Let P t be the path on t vertices. A bull is the graph obtained from a …

We give a new, stronger proof that there are only finitely many k-vertex-critical (P 5, gem)-
free graphs for all k. Our proof further refines the structure of these graphs and allows for the …

A graph G is k-vertex-critical if G has chromatic number k but every proper induced subgraph
of G has chromatic number less than k. The study of k-vertex-critical graphs for graph …

A graph G is k-vertex-critical if χ (G)= k but χ (G− v)< k for all v∈ V (G) where χ (G) denotes
the chromatic number of G. We show that there are only finitely many k-vertex-critical (P 3+ ℓ …

A graph $ G $ is $ k $-vertex-critical if $\chi (G)= k $ but $\chi (Gv)< k $ for all $ v\in V (G) $
and $(G, H) $-free if it contains no induced subgraph isomorphic to $ G $ or $ H $. We show …

A graph G is k-vertex-critical if χ (G)= k but χ (Gv)< k for all v∈ V (G), where χ (G) is the
chromatic number of G. A graph is (H 1, H 2)-free if it contains no induced subgraph …