Vertex-disjoint multiquadrilaterals in multigraphs

Huiling SHI; Yunshu GAO

doi:10.3868/s140-DDD-025-0012-x

Front. Math. China ›› 2025, Vol. 20 ›› Issue (3) : 135 -155. DOI: 10.3868/s140-DDD-025-0012-x

RESEARCH　ARTICLE

Vertex-disjoint multiquadrilaterals in multigraphs

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Abstract

A cycle of length 4 is called a quadrilateral and a multigraph is called standard if every edge in it has multiplicity at most 2. A quadrilateral with four multiedges is called heavy-quadrilateral. It is proved that if the minimum degree of M is at least $6 k − 2$ , then M contains k vertex-disjoint quadrilaterals, such that $k − 1$ of them are heavy-quadrilaterals and the remaining one is a quadrilateral with three multiedges, with only three exceptions.

Keywords

Multiquadrilateral / standard multigraph / minimum degree

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Huiling SHI,Yunshu GAO. Vertex-disjoint multiquadrilaterals in multigraphs. Front. Math. China, 2025, 20(3): 135-155 DOI:10.3868/s140-DDD-025-0012-x