The codiameter of a 2-connected graph |
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Authors: | Pei Wang |
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Institution: | a Department of Mathematics and Physics, China University of Petroleum-Beijing, Beijing 102249, China b Department of Mathematics, Renmin University of China, Beijing 100872, China |
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Abstract: | The codiameter of a graph is defined as the minimum, taken over all pairs of vertices u and v in the graph, of the maximum length of a (u,v)-path. A result of Fan Long cycles and the codiameter of a graph, I, J. Combin. Theory Ser. B 49 (1990) 151-180.] is that, for an integer c?3, if G is a 2-connected graph on n vertices with more than ((c+1)/2)(n-2)+1 edges, the codiameter of G is at least c. The result is best possible when n-2 is divisible by c-2. In this paper, we shall show that the bound ((c+1)/2)(n-2)+1 can be decreased when n-2 is not divisible by c-2. |
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Keywords: | Codiameter Edge-switching uv-cycle |
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