On The 2-Spanning Cyclability Of Honeycomb Toroidal Graphs

TL;DR

This paper investigates the 2-spanning cyclability property of honeycomb toroidal graphs, exploring conditions under which any two vertices can be separated into two cycles within a 2-factor.

Contribution

The paper provides a detailed analysis of 2-spanning cyclability in honeycomb toroidal graphs, a specific class of graphs, which was not previously studied in this context.

Findings

Characterization of 2-spanning cyclability in honeycomb toroidal graphs

Conditions for the existence of 2-factors with two cycles separating any two vertices

New theoretical results on the structure of honeycomb toroidal graphs

Abstract

A graph $X$ is 2-spanning cyclable if for any pair of distinct vertices $u$ and $v$ there is a 2-factor of $X$ consisting of two cycles such that $u$ and $v$ belong to distinct cycles. In this paper we examine the 2-spanning cyclability of honeycomb toroidal graphs.