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A decomposition of a multigraph is a partition of its edges into subgraphs . It is called an -factorization if every is -regular and spanning. If is a subgraph of , a decomposition of is said to be enclosed in a decomposition of if, for every , is a subgraph of .Feghali and Johnson gave necessary and sufficient conditions for a given decomposition of to be enclosed in some 2-edge-connected -factorization of for some range of values for the parameters , , , , : , and either , or and and , or and . We generalize their result to every and . We also give some sufficient conditions for enclosing a given decomposition of in some 2-edge-connected -factorization of for every and , where is a constant that depends only on , and . 相似文献
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《Discrete Mathematics》2020,343(10):111996
A Gallai coloring of a complete graph is an edge coloring without triangles colored with three different colors. A sequence of positive integers is an -sequence if . An -sequence is a G-sequence if there is a Gallai coloring of with colors such that there are edges of color for all . Gyárfás, Pálvölgyi, Patkós and Wales proved that for any integer there exists an integer such that every -sequence is a G-sequence if and only if . They showed that and .We show that and give almost matching lower and upper bounds for by showing that with suitable constants , for all sufficiently large . 相似文献
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Let be an additive finite abelian group with exponent . Let be the Davenport constant of , the th Erd?s–Ginzburg–Ziv constant of , where is a positive integer. Recently, Gao, Han, Peng and Sun conjectured that holds if . Let be positive integers and an abelian -group with . Let . For any integer , we prove that This verifies the above conjecture in this case. We also provide asymptotically tight bounds for zero-sum invariants , and for a class of abelian groups with large exponent. 相似文献
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For a positive integer , a graph is -knitted if for each subset of vertices, and every partition of into (disjoint) parts for some , one can find disjoint connected subgraphs such that contains for each . In this article, we show that if the minimum degree of an -vertex graph is at least when , then is -knitted. The minimum degree is sharp. As a corollary, we obtain that -contraction-critical graphs are -connected. 相似文献
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In this paper, we study the long-time behavior of solutions of a reaction–diffusion model in a one-dimensional river network, where the river network has two branches, and the water flow speeds in each branch are the same constant . We show the existence of two critical values and 2 with , and prove that when , the population density in every branch of the river goes to 1 as time goes to infinity; when , then, as time goes to infinity, the population density in every river branch converges to a positive steady state strictly below 1; when , the species will be washed down the stream, and so locally the population density converges to 0. Our result indicates that only if the water-flow speed is suitably small (i.e., ), the species will survive in the long run. 相似文献
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