# More on even [a,b]-factors in graphs

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 1, page 193-204
- ISSN: 2083-5892

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topAbdollah Khodkar, and Rui Xu. "More on even [a,b]-factors in graphs." Discussiones Mathematicae Graph Theory 27.1 (2007): 193-204. <http://eudml.org/doc/270555>.

@article{AbdollahKhodkar2007,

abstract = {In this note we give a characterization of the complete bipartite graphs which have an even (odd) [a,b]-factor. For general graphs we prove that an a-edge connected graph G with n vertices and with δ(G) ≥ max\{a+1,an/(a+b) + a - 2\} has an even [a,b]-factor, where a and b are even and 2 ≤ a ≤ b. With regard to the edge-connectivity this result is slightly better than one of the similar results obtained by Kouider and Vestergaard in 2004 and unlike their results, this result has no restriction on the order of graphs.},

author = {Abdollah Khodkar, Rui Xu},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {[a,b]-factor; spanning graph; edge-connectivity},

language = {eng},

number = {1},

pages = {193-204},

title = {More on even [a,b]-factors in graphs},

url = {http://eudml.org/doc/270555},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Abdollah Khodkar

AU - Rui Xu

TI - More on even [a,b]-factors in graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 1

SP - 193

EP - 204

AB - In this note we give a characterization of the complete bipartite graphs which have an even (odd) [a,b]-factor. For general graphs we prove that an a-edge connected graph G with n vertices and with δ(G) ≥ max{a+1,an/(a+b) + a - 2} has an even [a,b]-factor, where a and b are even and 2 ≤ a ≤ b. With regard to the edge-connectivity this result is slightly better than one of the similar results obtained by Kouider and Vestergaard in 2004 and unlike their results, this result has no restriction on the order of graphs.

LA - eng

KW - [a,b]-factor; spanning graph; edge-connectivity

UR - http://eudml.org/doc/270555

ER -

## References

top- [1] M.-C. Cai, On some factor theorems of graphs, Discrete Math. 98 (1991) 223-229, doi: 10.1016/0012-365X(91)90378-F. Zbl0758.05073
- [2] M. Kouider and P.D. Vestergaard, On even [2,b] -factors in graphs, Australasian J. Combin. 27 (2003) 139-147. Zbl1026.05092
- [3] M. Kouider and P.D. Vestergaard, Even [a,b] -factors in graphs, Discuss. Math. Graph Theory 24 (2004) 431-441, doi: 10.7151/dmgt.1242. Zbl1063.05109
- [4] M. Kouider and P.D. Vestergaard, Connected factors in graphs - a survey, Graphs and Combin. 21 (2005) 1-26, doi: 10.1007/s00373-004-0587-7. Zbl1066.05110
- [5] L. Lovász, Subgraphs with prescribed valencies, J. Combin. Theory 8 (1970) 391-416, doi: 10.1016/S0021-9800(70)80033-3. Zbl0198.29201
- [6] D.B. West, Introduction to Graph Theory (Prentice-Hall, Inc, 2000).

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