Every 3-connected $$\{K_{1,3},N_{1,2,3}\}$$-free graph is Hamilton-connected |
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Authors: | Zhiquan Hu Shunzhe Zhang |
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Institution: | 1.Faculty of Mathematics and Statistics,Central China Normal University,Wuhan,China |
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Abstract: | A graph G is \(\{X,Y\}\)-free if it contains neither X nor Y as an induced subgraph. Pairs of connected graphs X, Y such that every 3-connected \(\{X,Y\}\)-free graph is Hamilton-connected have been investigated recently in (2002, 2000, 2012). In this paper, it is shown that every 3-connected \(\{K_{1,3},N_{1,2,3}\}\)-free graph is Hamilton-connected, where \(N_{1,2,3}\) is the graph obtained by identifying end vertices of three disjoint paths of lengths 1, 2, 3 to the vertices of a triangle. |
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