Graphs vertex-partitionable into strong cliques

Graphs vertex-partitionable into strong cliques

A graph is said to be well-covered if all its maximal independent sets are of the same size. In 1999, Yamashita and Kameda introduced a subclass of well-covered graphs, called localizable graphs and defined as graphs having a partition of the vertex set into strong cliques, where a clique in a graph is strong if it intersects all maximal independent sets. Yamashita and Kameda observed that all ...

∆-critical Graphs with Small High Vertex Cliques

We prove thatKχ(G) is the only vertex critical graphG with χ(G) ≥ ∆(G) ≥ 6 and ω(H(G)) ≤ ⌊ ∆(G) 2 ⌋ − 2. Here H(G) is the subgraph of G induced on the vertices of degree at least χ(G). Setting ω(H(G)) = 1 proves a conjecture of Kierstead and Kostochka.

About the Strong Perfect Graph Conjecture on circular partitionable graphs

Turán Numbers of Vertex-disjoint Cliques in r-Partite Graphs

graph is called a complete r-partite graph if its vertex set can be partitioned into r independent sets V1, . . . , Vr such that for any i = 1, 2, . . . , r every vertex in Vi is adjacent to all other vertices in Vj , j 6= i. We denote a complete r-partite graph with part sizes |Vi| = ni by Kn1,...,nr . For a graph G and a positive integer k we use kG to denote k vertex-disjoint copies of G. Gi...

Turán numbers of vertex-disjoint cliques in -partite graphs