Suppose we have a tournament with edges labelled so that the edges incident with any vertex have at most k distinct labels (and no vertex has outdegree 0). Let m be the minimal size of a subset of labels such that for any vertex there exists an outgoing edge labelled by one of the labels in the subs
A Complete Solution of a Problem of Bondy Concerning Multipartite Tournaments
β Scribed by Yubao Guo; Lutz Volkmann
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 257 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Our aim in this note is to prove a conjecture of Bondy, extending a classical theorem of Dirac to edge-weighted digraphs: if every vertex has out-weight at least 1 then the digraph contains a path of weight at least 1. We also give several related conjectures and results concerning heavy cycles in e
CONCERNING A PROBLEM OF H. SCHOLZ By ANDRZEJ MOSTOWSKI in Warsxawa G . ASSER in his recent article [l] has established a number of interesting results pertaining to a problem proposed by H. SCHOLZ [2]. The results of ASSER overlap in part with results which I have found in 1953 while attempting (uns
## Abstract We show that a complete multipartite graph is class one if and only if it is not eoverfull, thus determining its chromatic index.
## Abstract We determine necessary and sufficient conditions for a complete multipartite graph to admit a set of 1βfactors whose union is the whole graph and, when these conditions are satisfied, we determine the minimum size of such a set. Β© 2008 Wiley Periodicals, Inc. J Graph Theory 58:239β250,
## Abstract A set __S__ of edgeβdisjoint hamilton cycles in a graph __G__ is said to be __maximal__ if the edges in the hamilton cycles in __S__ induce a subgraph __H__ of __G__ such that __G__βββ__E__(__H__) contains no hamilton cycles. In this context, the spectrum __S__(__G__) of a graph __G__ i