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math.CO2025
Decomposition of Cliques into -Star-Forests
Jiaxi Nie, Yibo Ren, Hehui Wu
A -star-forest is a forest with at most connected components where each component is a star. Let be the minimum integer such that the complete graph on vertices…
math.CO2025
Bisections of graphs under degree constraints
Jie Ma, Hehui Wu
In this paper, we investigate the problem of finding {\it bisections} (i.e., balanced bipartitions) in graphs. We prove the following two results for {\it all} graphs : (1). …