Optimization problem for star covers of graphs without four cycles

Damjana Kokol Bukovšek; Polona Oblak; Helena Šmigoc

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arXiv · 2605.17383

Optimization problem for star covers of graphs without four cycles

Damjana Kokol Bukovšek·Polona Oblak·Helena Šmigoc

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Abstract

This work presents a study of star covers on graphs. Unlike traditional formulations that minimize the number of stars, our aim is to optimize the number of bipartite components used in the cover. This problem, motivated by a symmetric nonnegative trifactorization of matrices and the SNT-rank of graphs, is in general hard to solve. We consider a family of graphs that do not contain four cycles, and develop an algorithm to determine the SNT-rank of such graphs.

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Damjana Kokol Bukovšek, Polona Oblak, Helena Šmigoc. 2026-05-17. Optimization problem for star covers of graphs without four cycles. https://arxiv.org/abs/2605.17383

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