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 polynomialtime 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12140
 Bibcode:
 2021arXiv210912140J
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Discrete Mathematics;
 Computer Science  Data Structures and Algorithms
 EPrint:
 Sequel to arXiv:2109.11498