Vertex-disjoint stars in graphs

Katsuhiro Ota

Discussiones Mathematicae Graph Theory (2001)

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

Abstract

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.