Connectivity keeping stars or double-stars in 2-connected graphs |
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Authors: | Yingzhi Tian Jixiang Meng Hong-Jian Lai Liqiong Xu |
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Institution: | 1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, PR China;2. Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA;3. School of Science, Jimei University, Xiamen, Fujian 361021, PR China |
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Abstract: | In Mader (2010), Mader conjectured that for every positive integer and every finite tree with order , every -connected, finite graph with contains a subtree isomorphic to such that is -connected. In the same paper, Mader proved that the conjecture is true when is a path. Diwan and Tholiya (2009) verified the conjecture when . In this paper, we will prove that Mader’s conjecture is true when is a star or double-star and . |
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Keywords: | 2-Connected graphs Stars Double-stars Mader’s conjecture |
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