Tight factorizations of girth-$g$-regular graphs

TL;DR

This paper investigates the structure of girth-regular graphs with equal girth, degree, and chromatic index, focusing on 1-factorizations intersecting all girth cycles, with applications in decomposability, geometry, and optimization.

Contribution

It introduces new methods for 1-factorizations in girth-regular graphs and explores their applications in decomposability, geometry, and optimization problems.

Findings

Established conditions for 1-factorizations intersecting all girth cycles.

Connected girth-regular graphs to Hamiltonian decomposability.

Suggested applications in geometry and priority assignment.

Abstract

Girth-regular graphs with equal girth, regular degree and chromatic index are studied for the determination of 1-factorizations with each 1-factor intersecting every girth cycle. Applications to hamiltonian decomposability and to 3-dimensional geometry are given. Applications are suggested for priority assignment and optimization problems.