Let G n,m,k denote the space of simple graphs with n vertices, m edges, and minimum degree at least k, each graph G being equiprobable. Let G have property A k , if G contains (k -1)/2 edge disjoint Hamilton cycles, and, if k is even, a further edge disjoint matching of size n/2 . We prove that, for
A Minimum Degree Result for Disjoint Cycles and Forests in Graphs
โ Scribed by Gerald W. Schuster
- Book ID
- 105746895
- Publisher
- Springer-Verlag
- Year
- 1998
- Tongue
- English
- Weight
- 232 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0209-9683
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๐ SIMILAR VOLUMES
## Abstract Let $n\_1,n\_2,\ldots,n\_k$ be integers, $n=\sum n\_i$, $n\_i\ge 3$, and let for each $1\le i\le k$, $H\_i$ be a cycle or a tree on $n\_i$ vertices. We prove that every graph __G__ of order at least __n__ with $\sigma\_2(G) \ge 2( n-k) -1$ contains __k__ vertex disjoint subgraphs $H\_1'
A cycle C of a graph G is a D~-cycle if every component of G-V(C) has order less than 2. Using the notion of D~-cycles, a number of results are established concerning long cycles in graphs with prescribed toughness and minimum degree. Let G be a t-tough graph on n/> 3 vertices. If 6 > n/(t + 2) + 2-
For the bandwidth B(G) and the cyclic bandwidth B c (G) of a graph G, it is known that 1 2 B(G) ยฐBc (G) ยฐB(G). In this paper, the criterion conditions for two extreme cases B c (G) ร B(G) and B c (G) ร 1 2 B(G) are studied. From this, some exact values of B c (G) for special graphs can be obtained.