Computing the tree number of a cut-outerplanar graph

TL;DR

This paper investigates the minimal number of trees needed to cover all edges in cut-outerplanar graphs, a less-studied aspect of graph decompositions, expanding understanding beyond classical arboricity.

Contribution

It introduces the concept of the tree number for cut-outerplanar graphs and provides initial results or bounds for this parameter.

Findings

Defined the tree number for cut-outerplanar graphs

Established bounds or exact values for specific classes of these graphs

Extended graph decomposition theory to a new class of graphs

Abstract

While the notion of arboricity of a graph is well-known in graph theory, very few results are dedicated to the minimal number of trees covering the edges of a graph, called the tree number of a graph.