JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE COMPETITION NUMBERS OF HAMMING GRAPHS WITH DIAMETER AT MOST THREE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
THE COMPETITION NUMBERS OF HAMMING GRAPHS WITH DIAMETER AT MOST THREE
Park, Bo-Ram; Sano, Yoshio;
  PDF(new window)
 Abstract
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of important research problems in the study of competition graphs. In this paper, we compute the competition numbers of Hamming graphs with diameter at most three.
 Keywords
competition graph;competition number;edge clique cover;Hamming graph;
 Language
English
 Cited by
1.
THE COMPETITION NUMBERS OF HAMMING GRAPHS WITH DIAMETER AT MOST THREE,;;

대한수학회지, 2011. vol.48. 4, pp.691-702 crossref(new window)
1.
A Generalization of Opsut’s Lower Bounds for the Competition Number of a Graph, Graphs and Combinatorics, 2013, 29, 5, 1543  crossref(new windwow)
2.
The competition number of the complement of a cycle, Discrete Applied Mathematics, 2013, 161, 12, 1755  crossref(new windwow)
3.
Competition numbers of complete r-partite graphs, Discrete Applied Mathematics, 2012, 160, 15, 2271  crossref(new windwow)
4.
Transversals and competition numbers of complete multipartite graphs, Discrete Applied Mathematics, 2013, 161, 3, 435  crossref(new windwow)
 References
1.
H. H. Cho and S.-R. Kim, The competition number of a graph having exactly one hole, Discrete Math. 303 (2005), no. 1-3, 32-41. crossref(new window)

2.
J. E. Cohen, Interval Graphs and Food Webs: a finding and a problem, Document 17696-PR, RAND Corporation, Santa Monica, CA, 1968.

3.
J. E. Cohen, Food Webs and Niche Space, Princeton University Press, Princeton, NJ, 1978.

4.
S.-R. Kim, The competition number and its variants, Quo vadis, graph theory?, 313-326, Ann. Discrete Math., 55, North-Holland, Amsterdam, 1993.

5.
S.-R. Kim, On competition graphs and competition numbers, Commun. Korean Math. Soc. 16 (2001), no. 1, 1-24.

6.
S.-R. Kim, Graphs with one hole and competition number one, J. Korean Math. Soc. 42 (2005), no. 6, 1251-1264. crossref(new window)

7.
S.-R. Kim, J. Y. Lee, and Y. Sano, The competition number of a graph whose holes do not overlap much, Discrete Appl. Math. 158 (2010), no. 13, 1456-1460. crossref(new window)

8.
S.-R. Kim, B. Park, and Y. Sano, The competition numbers of Johnson graphs, Discuss. Math. Graph Theory 30 (2010), 449-459. crossref(new window)

9.
S.-R. Kim and F. S. Roberts, Competition numbers of graphs with a small number of triangles, Discrete Appl. Math. 78 (1997), no. 1-3, 153-162. crossref(new window)

10.
S.-R. Kim and Y. Sano, The competition numbers of complete tripartite graphs, Discrete Appl. Math. 156 (2008), no. 18, 3522-3524. crossref(new window)

11.
J. Y. Lee, S.-R. Kim, S.-J. Kim, and Y. Sano, The competition number of a graph with exactly two holes, Ars Combin. 95 (2010), 45-54.

12.
R. J. Opsut, On the computation of the competition number of a graph, SIAM J. Algebraic Discrete Methods 3 (1982), no. 4, 420-428. crossref(new window)

13.
B. Park, S.-R. Kim, and Y. Sano, On competition numbers of complete multi- partite graphs with partite sets of equal size, preprint RIMS-1644 October 2008. (http://www.kurims.kyoto-u.ac.jp/preprint/file/RIMS1644.pdf)

14.
B. Park, S.-R. Kim, and Y. Sano, The competition numbers of complete multipartite graphs and mutually orthog- onal Latin squares, Discrete Math. 309 (2009), no. 23-24, 6464-6469. crossref(new window)

15.
B. Park and Y. Sano, The competition numbers of ternary Hamming graphs, Appl. Math. Lett. 24 (2011), 1608-1613. crossref(new window)

16.
F. S. Roberts, Food webs, competition graphs, and the boxicity of ecological phase space, Theory and applications of graphs (Proc. Internat. Conf., Western Mich. Univ., Kala- mazoo, Mich., 1976), pp. 477-490. Lecture Notes in Math., Vol. 642, Springer, Berlin, 1978.

17.
Y. Sano, The competition numbers of regular polyhedra, Congr. Numer. 198 (2009), 211-219.

18.
Y.Wu and J. Lu, Dimension-2 poset competition numbers and dimension-2 poset double competition numbers, Discrete Appl. Math. 158 (2010), no. 6, 706-717. crossref(new window)