P3-Factorization of complete bipartite graphs
โ Scribed by Kazuhiko Ushio
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 344 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
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.
๐ SIMILAR VOLUMES
We conclude the study of complete K1,q-factorizations of complete bipartite graphs of the form Kn,n and show that, so long as the obvious Basic Arithmetic Conditions are satisfied, such complete factorizations must exist.
We present a necessary condition for a complete bipartite graph K,., to be K,.,-factorizable and a sufficient condition for K,,, to have a K,,,-factorization whenever k is a prime number. These two conditions provide Ushio's necessary and sufficient condition for K,,, to have a K,,,-factorization.
For a complete bipartite graph, the number of dependent edges in an acyclic orientation can be any integer from n-1 to e, where n and e are the number of vertices and edges in the graph. ## Ke3,words: Bipartite graph; Acyclic orientation Ill combinatorics we often ask whether an integer parameter
## Abstract Given a graph __G__, for each ฯ โ__V__(__G__) let __L__(ฯ ) be a list assignment to __G__. The wellโknown choice number __c__(__G__) is the least integer __j__ such that if |__L__(ฯ )| โฅ__j__ for all ฯ โ__V__(__G__), then __G__ has a proper vertex colouring ฯ with ฯ(ฯ ) โ __L__ (ฯ ) (โฯ โ__