Báo cáo toán học: "Rainbow Matching in Edge-Colored Graphs" pot

... for K 4 or a graph obtained from K k+2 by removing a matching. A survey on rainbow matchings and other rainbow subgraphs appears in [1]. Subgraphs whose edges have distinct colors have also been ... odd, every proper n-edge-coloring of the complete bipartite graph K n,n contains a rainbow perfect matching. Wang and Li [4] studied rainbow matchings in arbitrary edge-colored graphs. W...

Ngày tải lên: 08/08/2014, 11:20

... Lov´asz and M. D. Plummer, Matching Theory, Akad´emiai Kiad´o, Budapest, 1986 [6] H. Minc, Nonnegative Matrices, Wiley, 1988 [7] V. R¨odl and A. Ruci´nski, Perfect matchings in -regular graphs and ... perfect matchings of G satisfies (d − 2) n n! ≤ M(G) ≤ (d +2) n n!. Thus, the number of perfect matchings in any super (d, )-regular graph on 2n vertices is close to the expected number...

Ngày tải lên: 07/08/2014, 06:22

... two of which sharing an edge, h as an s-colored t -matching contained in its union. In the case r = 2 the conjecture is that a set of t+1 disjoint t-matchings has a t-rainbow matching. This is yet ... similar, with one main difference: instead of leaving each matching M i after o ne edge, we continue choosing edges from it, until all edges in some matching M j represented in K ha...

Ngày tải lên: 08/08/2014, 01:20

... rainbow if its edges have distinct colors. Recently rainbow subgraphs have received much attention, see the survey paper [8]. Here we are interested in rainbow matchings. The study of rainbow matchings ... graph. A rainbow matching of G is a matching in which no two edges have the same color. Let δ denote the minimum degree of G. We show that if |V (G)| ≥ 8δ 5 , then G has a rainbow m...

Ngày tải lên: 08/08/2014, 14:23

... matching (or one-factor) of G is a subgraph of G in which each vertex has degree at most one. A basic question in combinatorial optimization is, “What is the size of a maximum matching in a given ... The set of incidence vectors of the matchings of G have a convex hull which is equal to the polytope containing all x ∈ R E which satisfy the following the electronic journal of combina...

Ngày tải lên: 07/08/2014, 13:21

... circuit containing P also contains all the other ears of X, including Q. By the inductive hypothesis, H has a comb T  H , equivalent to T ∩ EH, that has a balanced circuit containing e and the ... theorem for matching covered graphs which plays an important role in matching theory. An ear decomposition of a matching covered graph G is a sequence G 0 , G 1 , . . . , G t of matching...

Ngày tải lên: 07/08/2014, 15:23

... the cycle containing the set {x 1 ,x 2 , ··· ,x k } by constructing a set of disjoint x i ,x i+1 -paths, using that ¯ L and ¯ R are k-linked. Note that in constructing each x i ,x i+1 -path, using a free edge ... now one matching with k + t edges between ¯ L and ¯ R. We call an edge of this matching a double if both its endvertices are in S and a single if exactly one endvertex is in...

Ngày tải lên: 07/08/2014, 07:21

... question of finding a combinatorial interpretation of the above identity (1.2). In this paper, we obtain a parity reversing involution on noncrossing trees that leads to a combinatorial interpretation ... ,i k )withi 1 ,i 2 being the minimum and second minimum numbers. In the second case, after breaking C  t , there is also a cycle (i 1 ,i 2 , ,i k ,j 1 ,j 2 , ,j p )withi 1 ,i 2 being the...

Ngày tải lên: 07/08/2014, 13:21

... Spence [11]. In this paper, we yet introduce another extension of strongly regular graphs, from a different direction. In 1966, Erd˝os, R´enyi, and S´os [1, 4] proved the following interesting result, ... vertices u, v in V i (i = 1, 2), then by Claim 2, µ = δ(u, v) ≥ |V 3−i | ≥ 2, contradicting µ = 1. Thus there is no pair of non-adjacent vertices in each V i . By Claim 2, G = K n , c...

Ngày tải lên: 07/08/2014, 15:23

... for bringing the main problem of this paper to my attention during an interesting discussion in Budapest, and to Ingo Schiermeyer for his help and remarks in Freiberg. I also enclose greetings ... the domination number of G, γ(G), which is the size of the smallest dominating set of G, i.e. the subset, say D, of V (G) such that each vertex in V (G)  D has a neighbour in D. The followi...

Ngày tải lên: 07/08/2014, 21:20