The join K~ V2K2 is the graph obtained by taking a copy ofK, ~ and two disjoint copies of K2, disjoint from K c, and joining every vertex of K, c to every vertex of 2K2. In this paper we show that for each positive integer n, the graph K, ~ V 2/(2 admits a p-valuation and has gracefulness 4n + 3. Fu
3K2-decomposition of a graph
β Scribed by A. Bialostocki; Y. Roditty
- Publisher
- Akadmiai Kiad
- Year
- 1982
- Tongue
- English
- Weight
- 338 KB
- Volume
- 40
- Category
- Article
- ISSN
- 1588-2632
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π SIMILAR VOLUMES
We prove that, for every integer k >~ 2, every graph has an edge-partition into 5k 2 log k sets, each of which is the edge-set of a graph with all degrees congruent to 1 mod k. This answers a question of Pyber. Pyber proved that every graph G has an edge-partition into four sets, each of which is
## Abstract We show via an exhaustive computer search that there does not exist a (__K__~6~β__e__)βdecomposition of __K__~29~. This is the first example of a nonβcomplete graph __G__ for which a __G__βdecomposition of __K__~2|E(G)|+__1__~ does not exist. Β© 2009 Wiley Periodicals, Inc. J Combin Desi
A noncomplete graph G is called an (n, k)-graph if it is n-connected and G&X is not (n&|X | +1)-connected for any X V(G) with |X | k. Mader conjectured that for k 3 the graph K 2k+2 -(1-factor) is the unique (2k, k)-graph. We settle this conjecture for k 4.