Vertex-disjoint stars in graphs

Katsuhiro Ota

Discussiones Mathematicae Graph Theory (2001)

  • Volume: 21, Issue: 2, page 179-185
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Katsuhiro Ota. "Vertex-disjoint stars in graphs." Discussiones Mathematicae Graph Theory 21.2 (2001): 179-185. <http://eudml.org/doc/270550>.

@article{KatsuhiroOta2001,
abstract = {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.},
author = {Katsuhiro Ota},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {stars; vertex-disjoint copies; minimum degree; vertex-disjoint stars},
language = {eng},
number = {2},
pages = {179-185},
title = {Vertex-disjoint stars in graphs},
url = {http://eudml.org/doc/270550},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Katsuhiro Ota
TI - Vertex-disjoint stars in graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2001
VL - 21
IS - 2
SP - 179
EP - 185
AB - 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.
LA - eng
KW - stars; vertex-disjoint copies; minimum degree; vertex-disjoint stars
UR - http://eudml.org/doc/270550
ER -

References

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  1. [1] N. Alon and E. Fischer, Refining the graph density condition for the existence of almost K-factors, Ars Combin. 52 (1999) 296-308. Zbl0977.05103
  2. [2] N. Alon and R. Yuster, H-Factors in dense graphs, J. Combin. Theory (B) 66 (1996) 269-282, doi: 10.1006/jctb.1996.0020. Zbl0855.05085
  3. [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. Zbl0118.19001
  4. [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. Zbl0111.35901
  5. [5] H. Enomoto, Graph decompositions without isolated vertices, J. Combin. Theory (B) 63 (1995) 111-124, doi: 10.1006/jctb.1995.1007. Zbl0834.05046
  6. [6] Y. Egawa and K. Ota, Vertex-disjoint claws in graphs, Discrete Math. 197/198 (1999) 225-246. 
  7. [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. [8] A. Hajnal and E. Szemerédi, Proof of a conjecture of P. Erdős, Colloq. Math. Soc. János Bolyai 4 (1970) 601-623. Zbl0217.02601
  9. [9] J. Komlós, Tiling Turán theorems, Combinatorica 20 (2000) 203-218. Zbl0949.05063

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