On generating $k$-factorable graphic sequences with connected (resp.no connected) $k$-factors

TL;DR

This paper investigates methods for generating graphic sequences that can be decomposed into $k$-factors, focusing on whether these factors are connected or disconnected, contributing to graph theory and network design.

Contribution

It introduces new techniques for generating $k$-factorable graphic sequences with specified connectivity properties of their $k$-factors.

Findings

Established criteria for connected $k$-factors in generated sequences.

Developed algorithms for generating sequences with no connected $k$-factors.

Provided theoretical insights into the structure of $k$-factorable graphic sequences.

Abstract

In this note, we consider the problem of generating $k$-factorable graphic sequences with connected (resp. no connected) $k$-factors.