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,;;;

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

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