On Tuza's conjecture in co-chain graphs

TL;DR

This paper proves Tuza's conjecture for a specific subclass of interval graphs called co-chain graphs with even-sized partitions, expanding the classes of graphs where the conjecture holds.

Contribution

It establishes the validity of Tuza's conjecture for co-chain graphs with even partitions, a subclass of interval graphs, which was previously unresolved.

Findings

Tuza's conjecture holds for co-chain graphs with even partitions.

The result extends the classes of graphs satisfying Tuza's conjecture.

Provides new insights into the structure of co-chain graphs.

Abstract

In 1981, Tuza conjectured that the cardinality of a minimum set of edges that intersects every triangle of a graph is at most twice the cardinality of a maximum set of edge-disjoint triangles. This conjecture have been proved for several important graph classes, as planar graphs, tripartite graphs, among others. However, it remains open on other important classes of graphs, as chordal graphs. Furthermore, it remains open for main subclasses of chordal graphs, as split graphs and interval graphs. In this paper, we show that Tuza's conjecture is valid for co-chain graphs with even number of vertices in both sides of the partition, a known subclass of interval graphs.