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Minimum degree, leaf number and traceability

Show simple item record Mukwembi, Simon 2017-09-06T07:35:23Z 2017-09-06T07:35:23Z 2013-03-26
dc.identifier.citation Mukwembi, S. (2013). Minimum degree, leaf number and traceability. Czechoslovak Mathematical Journal, 63 (2), 539-545. en_US
dc.identifier.issn 1572-9141
dc.description This paper was written during the author’s Sabbatical visit at the University of Zimbabwe, Harare. en_US
dc.description.abstract Let G be a finite connected graph with minimum degree δ. The leaf number L (G) of G is defined as the maximum number of leaf vertices contained in a spanning tree of G. We prove that if δ >12(L (G) + 1), then G is 2-connected. Further, we deduce, for graphs of girth greater than 4, that if δ>12(L (G) + 1), then G contains a spanning path. This provides a partial solution to a conjecture of the computer program Graffiti.pc [DeLaVi ̃na and Waller, Spanning trees with many leaves and average distance, Electron. J. Combin. 15 (2008), 1–16]. For G claw-free, we show that if δ >12(L (G) + 1), then G is Hamiltonian. This again confirms, and even improves, the conjecture of Graffiti.pc for this class of graphs. en_US
dc.description.sponsorship National Research Foundation and the University of KwaZulu-Natal en_US
dc.language.iso en_ZW en_US
dc.publisher Institute of Mathematics of the Czech Academy of Sciences en_US
dc.subject interconnection network en_US
dc.subject graph en_US
dc.subject leaf number en_US
dc.subject traceability en_US
dc.subject Hamiltonicity en_US
dc.subject Graffiti.pc en_US
dc.title Minimum degree, leaf number and traceability en_US
dc.type Article en_US
dc.contributor.authoremail en_US

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