Feb 19, 2015 · To test if a graph G is k -critical, we first test if it is k -vertex-critical by considering the chromatic number of G − v for each vertex v ∈ ...

Jan 2, 2013 · Given a graph G, let G ∨ u denote the graph obtained from G by adding a new vertex u and adding all edges between u and the vertices of G.

We present a polynomial-time algorithm determining whether or not, for a fixed k, a P 5 -free graph can be k-colored. If such a coloring exists, the algorithm ...

Apr 10, 2021 · In this paper, we initiate a systematic study of the finiteness of k-vertex-critical graphs in subclasses of -free graphs.

With respect to a hereditary class of graphs, a -chromatic graph is said to be -critical if every proper subgraph of belonging to is colorable.

Feb 23, 2021 · Abstract. Given two graphs H1 and H2, a graph G is (H1, H2)-free if it contains no induced subgraph isomorphic to H1 or H2.

Jun 6, 2023 · We construct a new infinite families of k-vertex-critical (P5,C5)-free graphs for all k ≥ 6. Our construction generalizes known constructions ...

Feb 23, 2021 · Abstract. Given two graphs H1 and H2, a graph G is (H1, H2)-free if it contains no induced subgraph isomorphic to H1 or H2.

Constructions of k-critical P5-free graphs. Year: 2015. Type of Publication: Journal Article. Author(s):. Chinh Hoang,Brian Moore,Daniel Recoskie,Joe Sawada ...

Constructions of k-critical P5-free graphs · Mathematics. Discret. Appl. Math. · 2015.