P4k−1-factorization of bipartite multigraphs
✍ Scribed by Jian Wang; Beiliang Du
- Publisher
- SP Science China Press
- Year
- 2006
- Tongue
- English
- Weight
- 206 KB
- Volume
- 49
- Category
- Article
- ISSN
- 1674-7283
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## Abstract We prove a necessary and sufficient condition for a regular bipartite multigraph to contain a 1‐factor including one specified set of independent edges and avoiding another specified set of edges. © 1995 John Wiley & Sons, Inc.
Usual edge colorings have been generalized in various ways; we wilI consider here essentially good edge colorings as well as equitable edge colorings. It is known that bipartite multigraphs present the property of having an equitable k-coloring for each k 3 2. This implies that they also have a good
P,-factorization of K,,,, is (i) m + n -0 (mod 3), (ii) m < 2n, (iii) n s 2m and (iv) 3mn/2(m + n) is an integer.