Vertex-disjoint stars in graphs

• Autorzy: Katsuhiro Ota
• Języki publikacji: EN

Abstrakty

EN

In this paper, we give a sufficient condition for a graph to contain vertex-disjoint stars of a given size. It is proved that if the minimum degree of the graph is at least k+t-1 and the order is at least (t+1)k + O(t²), then the graph contains k vertex-disjoint copies of a star $K_{1,t}$. The condition on the minimum degree is sharp, and there is an example showing that the term O(t²) for the number of uncovered vertices is necessary in a sense.

Słowa kluczowe

EN

stars; vertex-disjoint copies; minimum degree

Kategorie tematyczne

• 05C70: Factorization, matching, partitioning, covering and packing
• 05C35: Extremal problems

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2001
• Tom: 21
• Numer: 2
• Strony: 179-185

Daty

wydano

2001

otrzymano

2000-09-27

poprawiono

2001-03-19

Twórcy

autor

Katsuhiro Ota

• Department of Mathematics, Keio University, Yokohama, 223-8522 Japan

Bibliografia

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• [3] K. Corrádi and A. Hajnal, On the maximal number of independent circuits in a graph, Acta Math. Acad. Sci. Hunger. 14 (1963) 423-443, doi: 10.1007/BF01895727.
• [4] G.A. Dirac, On the maximal number of independent triangle in graphs, Abh. Sem. Univ. Hamburg 26 (1963) 78-82, doi: 10.1007/BF02992869.
• [5] H. Enomoto, Graph decompositions without isolated vertices, J. Combin. Theory (B) 63 (1995) 111-124, doi: 10.1006/jctb.1995.1007.
• [6] Y. Egawa and K. Ota, Vertex-disjoint claws in graphs, Discrete Math. 197/198 (1999) 225-246.
• [7] H. Enomoto, A. Kaneko and Zs. Tuza, P₃-factors and covering cycles in graphs of minimum degree n/3, Colloq. Math. Soc. János Bolyai 52 (1987) 213-220.
• [8] A. Hajnal and E. Szemerédi, Proof of a conjecture of P. Erdős, Colloq. Math. Soc. János Bolyai 4 (1970) 601-623.
• [9] J. Komlós, Tiling Turán theorems, Combinatorica 20 (2000) 203-218.

Identyfikatory

DOI

10.7151/dmgt.1142