The Weisfeiler-Leman dimension of chordal bipartite graphs without bipartite claw

TL;DR

This paper proves that chordal bipartite graphs without bipartite claw have Weisfeiler-Leman dimension at most 3, using coherent configurations, advancing understanding of graph isomorphism complexity.

Contribution

It establishes a bound on the Weisfeiler-Leman dimension for a specific class of bipartite graphs, linking structural properties to algorithmic complexity.

Findings

Weisfeiler-Leman dimension is at most 3 for the class

Chordal bipartite graphs without bipartite claw are characterized

Proof utilizes coherent configurations

Abstract

A graph $X$ is said to be chordal bipartite if it is bipartite and contains no induced cycle of length at least $6$. It is proved that if $X$ does not contain bipartite claw as an induced subgraph, then the Weisfeiler-Leman dimension of $X$ is at most $3$. The proof is based on the theory of coherent configurations.