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Mathematics > Combinatorics
Title: Three aspects of the MSTCI problem
(Submitted on 18 Jan 2023 (v1), last revised 22 Apr 2024 (this version, v2))
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. The MSTCI problem consists in finding a spanning tree that has the least number of such non-empty intersections and the instersection number is the number of non-empty intersections of a solution. In this article we consider three aspects of the problem in a general context (i.e. for arbitrary connected graphs). The first presents two lower bounds of the intersection number. The second compares the intersection number of graphs that differ in one edge. The last is an attempt to generalize a recent result for graphs with a universal vertex.
Submission history
From: Manuel Dubinsky [view email][v1] Wed, 18 Jan 2023 16:42:00 GMT (139kb,D)
[v2] Mon, 22 Apr 2024 13:27:28 GMT (139kb,D)
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