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arXiv · 2312.15902

Eigenvalues and factors: a survey

Dandan Fan·Huiqiu Lin·Hongliang Lu·Suil O
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Abstract

A factor of a graph is a spanning subgraph satisfying some given conditions. An earlier survey of factors can be traced back to the Akiyama and Kano [J. Graph Theory, 1985, 9: 1-42] in which they described the characterization of factors in (bipartite) graphs and digraphs, respectively. Soon after, Kouider and Vestergaard summarized the findings related to connected factors [Graphs Combin., 2005, 21(1): 1-26]. Plummer extended the aforementioned research by providing a comprehensive overview of progress made in the study of graph factors and factorization from 1985 to 2003 [Discrete Math., 2007, 7-8: 791-821]. In this paper, we aim to summarize the relevant results regarding factors from the perspective of eigenvalues.

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Dandan Fan, Huiqiu Lin, Hongliang Lu, Suil O. 2023-12-26. Eigenvalues and factors: a survey. https://arxiv.org/abs/2312.15902

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