Vertebrate interval graphs

Abstract

A vertebrate interval graph is an interval graph in which the maximum size of a set of independent vertices equals the number of maximal cliques. For any fixed $v\ge 1$, there is a polynomial-time algorithm for deciding whether a vertebrate interval graph admits a vertex partition into two induced subgraphs with claw number at most $v$. In particular, when $v=2$, whether a vertebrate interval graph can be partitioned into two proper interval graphs can be decided in polynomial time.

Sequel to arXiv:2109.11498

References in corpus (1)

• Partitioning an interval graph into subgraphs with small claws