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Journals and Conferences
In this paper graphs are assumed to be finite, undirected and without loops, though they may contain multiple edges. We will also consider pseudo-graphs, which, in contrast with graphs, may contain… (More)
For k ≥ 1 and a graphG let νk(G) denote the size of a maximum k-edge-colorable subgraph of G. Mkrtchyan, Petrosyan and Vardanyan proved that ν2(G) ≥ 4 5 · |V (G)|, ν3(G) ≥ 7 6 · |V (G)| for any cubic… (More)
The resistance r(G) of a graph G is the minimum number of edges that have to be removed from G to obtain a graph which is ∆(G)-edge-colorable. The paper relates the resistance to other parameters… (More)
For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its… (More)
I prove that in a tree in which the distance between any two endpoints is even, there is a maximum proper partial 0 − 1 coloring such that the edges colored by 0 form a maximum matching.
A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs contain a perfect matching.
A graph G is class II, if its chromatic index is at least ∆ + 1. Let H be a maximum ∆-edge-colorable subgraph of G. The paper proves best possible lower bounds for |E(H)| |E(G)| , and structural… (More)
We show that any 2−factor of a cubic graph can be extended to a maximum 3−edge-colorable subgraph. We also show that the sum of sizes of maximum 2− and 3−edge-colorable subgraphs of a cubic graph is… (More)
If G and H are two cubic graphs, then we write H ≺ G if G admits a proper edge-coloring f with edges of H, such that for each vertex x of G, there is a vertex y of H with f(∂G(x)) = ∂H(y). Let P and… (More)
For a graph G, consider the pairs of edge-disjoint matchings whose union consists of as many edges as possible. Let H be the largest matching among such pairs. Let M be a maximum matching of G. We… (More)