Disjoint matchings of graphs
نویسندگان
چکیده
منابع مشابه
TRACTATUS on disjoint matchings in cubic graphs
In early 70s Berge conjectured that any bridgeless cubic graph contains five perfect matchings such that each edge belongs to at least one of them. In 1972 Fulkerson conjectured that, in fact, we can find six perfect matchings containing each edge exactly twice. By introducing the concept of an r-graph (a remarkable generalization of one of bridgeless cubic graph) Seymour in 1979 conjectured th...
متن کاملCubic Graphs, Disjoint Matchings and Some Inequalities
For k = 2, 3 and a cubic graph G 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)| [13]. They were also able to show that ν2(G) + ν3(G) ≥ 2 · |V (G)| [3] and ν2(G) ≤ |V (G)|+2·ν3(G) 4 [13]. In the present work, we show that the last two inequalities imply the first two of them. Moreo...
متن کاملOn disjoint matchings in cubic graphs
In the 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 loops. Thus graphs are pseudo-graphs. We accept the convention that a loop contributes to the degree of a vertex by two. The set of vertices and edges of a pseudo-graph G will be denoted by V (G) and ...
متن کاملOn disjoint perfect tree-matchings in random graphs
For an arbitrary tree T, a T-matching in G is a set of vertex-disjoint subgraphs of G which are isomorphic to T. A T-matching which is a spanning subgraph of G is called a perfect T-matching. For any t-vertex tree T we find a threshold probability function jj = jj( n) for the existence of r edge-disjoint perfect T-matchings in a random graph G(n,p).
متن کاملPerfect Matchings in Edge-Transitive Graphs
We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1977
ISSN: 0095-8956
DOI: 10.1016/0095-8956(77)90066-1