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## Discussiones Mathematicae Graph Theory

2015 | 35 | 1 | 191-196
Tytuł artykułu

### On a Spanning k-Tree in which Specified Vertices Have Degree Less Than k

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
A k-tree is a tree with maximum degree at most k. In this paper, we give a degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than k. We denote by σk(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k ≥ 3 and s ≥ 0 be integers, and suppose G is a connected graph and σk(G) ≥ |V (G)|+s−1. Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree less than k. The degree condition is sharp.
Słowa kluczowe
EN
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
191-196
Opis fizyczny
Daty
wydano
2015-02-01
otrzymano
2013-10-16
poprawiono
2014-01-31
zaakceptowano
2014-01-31
online
2015-02-06
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autor
Bibliografia
• [1] M.N. Ellingham, Y. Nam and H.-J. Voss, Connected (g, f)-factors, J. Graph Theory 39 (2002) 62-75. doi:10.1002/jgt.10019[Crossref]
• [2] H. Enomoto and K. Ozeki, The independence number condition for the existence of a spanning f-tree, J. Graph Theory 65 (2010) 173-184. doi:10.1002/jgt.20471[Crossref]
• [3] H. Matsuda and H.Matsumura, On a k-tree containing specified leaves in a graph, Graphs Combin. 22 (2006) 371-381. doi:10.1007/s00373-006-0660-5[WoS][Crossref]
• [4] H.Matsuda and H.Matsumura, Degree conditions and degree bounded trees, Discrete Math. 309 (2009) 3653-3658. doi:10.1016/j.disc.2007.12.099[Crossref]
• [5] V. Neumann-Lara and E. Rivera-Campo, Spanning trees with bounded degrees, Com- binatorica 11 (1991) 55-61. doi:10.1007/BF01375473[Crossref][WoS]
• [6] O. Ore, Note on Hamilton circuits, Amer. Math. Monthly 67 (1960) 55.
• [7] O. Ore, Hamilton connected graphs, J. Math. Pures Appl. 42 (1963) 21-27. doi:10.2307/2308928[Crossref]
• [8] S. Win, Existenz von ger¨usten mit vorgeschriebenem maximalgrad in graphen, Abh. Math. Seminar Univ. Hamburg 43 (1975) 263-267. doi:10.1007/BF02995957[Crossref]
• [9] S. Win, On a connection between the existence of k-trees and the toughness of a graph, Graphs Combin. 5 (1989) 201-205. doi:10.1007/BF01788671 [Crossref]
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Bibliografia
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