Spectral analogues of Moon-Moser's theorem on Hamilton paths in bipartite graphs

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• 作者：Binlong Li^a ; ^{libinlong@mail.nwpu.edu.cn} ; Bo Ning^b ; ^{bo.ning@tju.edu.cn}
• 关键词：05C50 ; 15A18 ; 05C38
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：515
• 期：Complete
• 页码：180-195
• 全文大小：367 K
• 卷排序：515

文摘

In 1962, Erdős proved a theorem on the existence of Hamilton cycles in graphs with given minimum degree and number of edges. Significantly strengthening in case of balanced bipartite graphs, Moon and Moser proved a corresponding theorem in 1963. In this paper we establish several spectral analogues of Moon and Moser's theorem on Hamilton paths in balanced bipartite graphs and nearly balanced bipartite graphs. One main ingredient of our proofs is a structural result of its own interest, involving Hamilton paths in balanced bipartite graphs with given minimum degree and number of edges.