Edge-disjoint cycles in regular directed graphs
โ Scribed by Alon, Noga; McDiarmid, Colin; Molloy, Michael
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 356 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
We prove that any k-regular directed graph with no parallel edges contains a collection of at least fl(k2) edge-disjoint cycles; we conjecture that in fact any such graph contains a collection of at least ( lCi1 ) disjoint cycles, and note that this holds for k 5 3. o 1996
๐ SIMILAR VOLUMES
A graph is claw-free if it does not contain K l , 3 as an induced subgraph. It is Kl,,-free if it does not contain K l , r as an induced subgraph. We show that if a graph is Kl,,-free ( r 2 4), only p + 2r -1 edges are needed to insure that G has t w o disjoint cycles. As an easy consequence w e ge
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
It is shown that, for โ ) 0 and n ) n โ , any complete graph K on n vertices 0 ' ลฝ . whose edges are colored so that no vertex is incident with more than 1 y 1r 2 y โ n edges of the same color contains a Hamilton cycle in which adjacent edges have distinct colors. Moreover, for every k between 3 and
Let G be a graph of order n satisfying d(u) + d(v) โฅ n for every edge uv of G. We show that the circumference-the length of a longest cycle-of G can be expressed in terms of a certain graph parameter, and can be computed in polynomial time. Moreover, we show that G contains cycles of every length be