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arXiv · 2308.01456

Decomposing a signed graph into rooted circuits

Rose McCarty
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Abstract

We prove a precise min-max theorem for the following problem. Let $G$ be an Eulerian graph with a specified set of edges $S \subseteq E(G)$, and let $b$ be a vertex of $G$. Then what is the maximum integer $k$ so that the edge-set of $G$ can be partitioned into $k$ non-zero $b$-trails? That is, each trail must begin and end at $b$ and contain an odd number of edges from~$S$. This theorem is motivated by a connection to vertex-minors and yields two conjectures of Máčajová and Škoviera as corollaries.

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Rose McCarty. 2025-06-09. Decomposing a signed graph into rooted circuits. https://arxiv.org/abs/2308.01456

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