排序方式: 共有2条查询结果,搜索用时 0 毫秒
1
1.
We show that any connected regular graph with d+1 distinct eigenvalues and odd-girth 2d+1 is distance-regular, and in particular that it is a generalized odd graph. 相似文献
2.
J.M. McDonald 《Discrete Mathematics》2009,309(8):2077-2214
Let G be a multigraph with maximum degree Δ and maximum edge multiplicity μ. Vizing’s Theorem says that the chromatic index of G is at most Δ+μ. If G is bipartite its chromatic index is well known to be exactly Δ. Otherwise G contains an odd cycle and, by a theorem of Goldberg, its chromatic index is at most , where go denotes odd-girth. Here we prove that a connected G achieves Goldberg’s upper bound if and only if G=μCgo and (go−1)∣2(μ−1). The question of whether or not G achieves Vizing’s upper bound is NP-hard for μ=1, but for μ≥2 we have reason to believe that this may be answerable in polynomial time. We prove that, with the exception of μK3, every connected G with μ≥2 which achieves Vizing’s upper bound must contain a specific dense subgraph on five vertices. Additionally, if Δ≤μ2, we prove that G must contain K5, so G must be nonplanar. These results regarding Vizing’s upper bound extend work by Kierstead, whose proof technique influences us greatly here. 相似文献
1