RANDOMLY ORTHOGONAL FACTORIZATIONS OF (0,mf - (m - 1)r)-GRAPHS

- Journal title : Journal of the Korean Mathematical Society
- Volume 45, Issue 6, 2008, pp.1613-1622
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2008.45.6.1613

Title & Authors

RANDOMLY ORTHOGONAL FACTORIZATIONS OF (0,mf - (m - 1)r)-GRAPHS

Zhou, Sizhong; Zong, Minggang;

Zhou, Sizhong; Zong, Minggang;

Abstract

Let G be a graph with vertex set V(G) and edge set E(G), and let g, f be two nonnegative integer-valued functions defined on V(G) such that for every vertex x of V(G). We use to denote the degree of a vertex x of G. A (g, f)-factor of G is a spanning subgraph F of G such that for every vertex x of V(F). In particular, G is called a (g, f)-graph if G itself is a (g, f)-factor. A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {, , ..., } be a factorization of G and H be a subgraph of G with mr edges. If , , has exactly r edges in common with H, we say that F is r-orthogonal to H. If for any partition {, , ..., } of E(H) with there is a (g, f)-factorization F = {, , ..., } of G such that , , then we say that G has (g, f)-factorizations randomly r-orthogonal to H. In this paper it is proved that every (0, mf - (m - 1)r)-graph has (0, f)-factorizations randomly r-orthogonal to any given subgraph with mr edges if for any .

Keywords

graph;subgraph;factor;orthogonal factorization;

Language

English

Cited by

1.

NOTE ON CONNECTED (g, f)-FACTORS OF GRAPHS,Zhou, Sizhong;Wu, Jiancheng;Pan, Quanru;

Journal of applied mathematics & informatics, 2010. vol.28. 3_4, pp.909-912

References

1.

J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier Publishing Co., Inc., New York, 1976

2.

H. Feng, On orthogonal (0, f)-factorizations, Acta Math. Sci. (English Ed.) 19 (1999), no. 3, 332-336

4.

G. Li and G. Liu, (g, f)-factorization orthogonal to any subgraph, Sci. China Ser.A 27 (1997), no. 12, 1083-1088

5.

G. Liu, (g, f)-factorizations orthogonal to a star in graphs, Sci. China Ser. A 38 (1995), no. 7, 805-812

7.

G. Liu and B. Zhu, Some problems on factorizations with constraints in bipartite graphs, Discrete Appl. Math. 128 (2003), no. 2-3, 421-434

9.

T. Tokuda, Connected [a, b]-factors in $K_{1.n}$ -free graphs containing an [a, b]-factor, Discrete Math. 207 (1999), no. 1-3, 293-298

10.

J. Yuan and J. Yu, Random (m, $\gamma$ )-orthogonal (g, f)-factorizable graphs, Appl. Math. A J. Chinese Univ. (Ser. A) 13 (1998), no. 3, 311-318