In this article, we show that every simple r-regular graph G admits a balanced P 4 -decomposition if r โก 0(mod 3) and G has no cut-edge when r is odd. We also show that a connected 4-regular graph G admits a P 4 -decomposition if and only if |E(G)| โก 0(mod 3) by characterizing graphs of maximum degr
r-Regular, r-connected decompositions of complete graphs
โ Scribed by H. Fleischner; W. R. Johnstone; A. J. W. Hilton
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 139 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
โฆ Synopsis
If rjn ร 1 and rn is even, then K n can be expressed as the union of t nร1 r edgedisjoint isomorphic r-regular r-connected factors.
๐ SIMILAR VOLUMES
The circulant G,(al,. . . , ak), where 0 < al < ... < a k < ( n + 1 ) / 2 , is defined as the vertex-transitive graph that has vertices ifal,. . . ,if a k (mod n) adjacent to each vertex i. In this work we show that the connected circulants of degree at least three contain all even cycles. In additi
It is shown that for each r G 3, a random r-regular graph on 2 n vertices is equivalent in a certain sense to a set of r randomly chosen disjoint perfect matchings of the 2 n vertices, as n ยช ฯฑ. This equivalence of two sequences of probabilistic spaces, called contiguity, occurs when all events almo
If G is a graph on n vertices and r 2 2, w e let m,(G) denote the minimum number of complete multipartite subgraphs, with r or fewer parts, needed to partition the edge set, f(G). In determining m,(G), w e may assume that no two vertices of G have the same neighbor set. For such reduced graphs G, w
In this paper w e prove the following result. Let ml 2 m2 2 ... 2 ml be nonnegative integers. A necessary and sufficient condition for the complete graph K,, to be decomposed into stars S,,, , S