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- Title
On ƒ-Edge Cover Coloring of Nearly Bipartite Graphs.
- Authors
JINBO LI; GUIZHEN LIU
- Abstract
Let G(V,E) be a graph, and let ƒ be an integer function on V with 1 ≤ ƒ(v) ≤ d(v) to each vertex v ϵ V . An ƒ-edge cover coloring is an edge coloring C such that each color appears at each vertex v at least ƒ(v) times. The ƒ-edge cover chromatic index of G, denoted by χ′ƒc(G), is the maximum number of colors needed to ƒ-edge cover color G. It is well-known that minvϵV ⌊d(v)-μ(v)/ƒ(v)⌋ ≤χ′ƒc(G) ≤ δƒ, where μ(v) is the multiplicity of v and δƒ = min{⌊d(v)/ƒ(v)⌋ : v ϵ V(G)}. If χ′ƒc = δƒ, then G is of ƒc-class 1, otherwise G is of ƒc-class 2. In this paper, we give some new sufficient conditions for a nearly bipartite graph to be of ƒc-class 1.
- Subjects
BIPARTITE graphs; FINITE element method; VECTOR spaces; CHROMATIC polynomial; MATHEMATICAL optimization; COMPUTER networks
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2011, Vol 34, Issue 2, p247
- ISSN
0126-6705
- Publication type
Article