Quantitative characteristics of cycles and their relations with stretch and spanning tree congestion

TL;DR

This paper introduces the support number, a new quantitative measure of cycles in graphs, and explores its relationship with stretch and spanning tree congestion, providing polynomial approximation algorithms for these parameters.

Contribution

The paper defines the support number and cycle width, establishing their relations to stretch and spanning tree congestion, along with polynomial approximation methods.

Findings

Support number and cycle width are new graph cycle characteristics.

Established relationships between support number, stretch, and spanning tree congestion.

Provided polynomial approximation algorithms for the support number.

Abstract

The main goal of this article is to introduce new quantitative characteristics of cycles in finite simple connected graphs and to establish relations of these characteristics with the stretch and spanning tree congestion of graphs. The main new parameter is named the support number. We give a polynomial approximation algorithm for the support number with the aid of yet another characteristic we introduce, named the cycle width of the graph.