Minimum Spanning Tree Cycle Intersection Problem

TL;DR

This paper introduces the Minimum Spanning Tree Cycle Intersection Problem, which seeks a spanning tree minimizing the number of shared edges among cycles formed by adding non-tree edges, addressing a novel intersection minimization challenge.

Contribution

It formulates a new optimization problem focused on reducing cycle intersections in spanning trees, providing a foundation for further theoretical and algorithmic exploration.

Findings

Defined the MST cycle intersection problem formally.

Identified the problem's computational complexity.

Proposed initial approaches for minimizing cycle intersections.

Abstract

Consider a connected graph $G$ and let $T$ be a spanning tree of $G$. Every edge $e \in G-T$ induces a cycle in $T \cup \{e\}$. The intersection of two distinct such cycles is the set of edges of $T$ that belong to both cycles. We consider the problem of finding a spanning tree that has the least number of such non-empty intersections.