On strictly Chordality-k graphs

TL;DR

This paper introduces and studies the properties and algorithms related to strictly Chordality-k graphs, which generalize chordal and chordal bipartite graphs by constraining induced cycles to be exactly of length k.

Contribution

It initiates a structural and algorithmic exploration of SC_k graphs for k ≥ 5, extending the understanding of these graph classes.

Findings

Defined the class of SC_k graphs for k ≥ 5.

Established structural properties of SC_k graphs.

Developed algorithms for recognizing and analyzing SC_k graphs.

Abstract

Strictly Chordality-k graphs (SC_k graphs) are graphs which are either cycle free or every induced cycle is exactly k, for some fixed k, k \geq 3. Note that k = 3 and k = 4 are precisely the Chordal graphs and Chordal Bipartite graphs, respectively. In this paper, we initiate a structural and an algorithmic study of SCk, k \geq 5 graphs.