Connected k-factors in bipartite graphs

2018/08/08 by Yandong Bai, Binlong Li, Bai, Yandong +1 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1808.02660

openalex publication_date 2018/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k,l be two positive integers. An S_k,l is a graph obtained from disjoint K_1,k and K_1,l by adding an edge between the k-degree vertex in K_1,k and the l-degree vertex in K_1,l. An \em S_k,l-free graph is a graph containing no induced subgraph isomorphic to S_k,l. In this note, we show that, for any positive integers k,l with 2\leqslant k\leqslant l, there exists a constant c=c(k,l) such that every connected balanced S_k,l-free bipartite graph with minimum degree at least c contains a connected k-factor.

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