Three problems in connection with cycles on the butterfly graphs are studied in this paper. The first problem is to construct complete uniform cycle partitions for the butterfly graphs. Suppose that
Long cycles in critical graphs
โ Scribed by Noga Alon; Michael Krivelevich; Paul Seymour
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 57 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0364-9024
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๐ SIMILAR VOLUMES
In this article, we establish bounds for the length of a longest cycle C in a 2-connected graph G in terms of the minimum degree ฮด and the toughness t. It is shown that C is a Hamiltonian cycle or |C| โฅ (t + 1)ฮด + t.
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
## For a graph G and an integer an independent set of vertices in G}. Enomoto proved the following theorem. Let s โฅ 1 and let G be a (s + 2)-connected graph. Then G has a cycle of length โฅ min{|V (G)|, ฯ 2 (G) -s} passing through any path of length s. We generalize this result as follows. Let k โฅ