## 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
โฆ LIBER โฆ
Long paths through four vertices in a 2-connected graph
โ Scribed by Barovich, Mark V.
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 252 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0364-9024
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โฆ Synopsis
Let G be a 2-connected graph, let u and v be distinct vertices in V (G), and let X be a set of at most four vertices lying on a common (u
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We prove the following theorem: For a connected noncomplete graph Then through each edge of G there passes a cycle of length โฅ min{|V (G)|, ฯ(G) -1}.