Báo cáo toán học: "Rainbow matchings in properly edge colored graphs" pps

... 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 ... 05C15, 05C70 Abstract Let G be a properly edge colored graph. A rainbow matching of G is a matching in which no two edges have the same color. Let δ denote the minimum degree...

Ngày tải lên: 08/08/2014, 14:23

... 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 ... that there exists in H ′ a matching M of V 1 , containing the edge (x, y, z). Color all edges in M by color 1, and for every edge a = (p, q, r) colored 1 by f, if there exists...

Ngày tải lên: 08/08/2014, 01:20

... one of the edges incident with x will be a cutedge of G, a contradiction. Thus u and v are nonadjacent in G. Let G ′ = (G \ D) + uv, that is obtained from G by deleting D a nd adding an edge uv. ... with only 9 perfect matchings We prove that every claw-free cubic n-vertex graph with no cutedge has more than 2 n/12 perfect matchings. The graph should not have any cutedge; in Figure 1...

Ngày tải lên: 08/08/2014, 14:22

... graph G containing F i and any dominating set D in G, the set D has at least 9 vertices in V (F i ). If D contains neither x i nor y i , then by Claim 1 D must contain 3 vertices in each of V ... bound was proved in [2] by exploiting Reed’s techniques in [9] and examining some of the cases in Reed’s proof more carefully and adding a dis- charging argument. However, exploting Reed’...

Ngày tải lên: 07/08/2014, 15:22

... χ(G). Since there are no good cycles in G, therefore the coloring of V ( G )\S is proper. For each w ∈ Q\S, there is a w-colorful path in V (G)\S going downward in T t hro ugh P , by passing from ... child in P. For each w ∈ V (G)\Q, there is a w-colorful path in V (G)\S going upward in T by passing from each vertex to its parent. So for each w ∈ V (G)\S, there is a w-colorful pat...

Ngày tải lên: 08/08/2014, 12:23

... +2) n n!. Thus, the number of perfect matchings in any super (d, )-regular graph on 2n vertices is close to the expected number of such matchings in a random bipartite graph with edge probability d (which ... bound follows by applying the Stirling approximation formula for factorials. It is worth noting that since every -regular graph with density d and 2n vertices contains, in...

Ngày tải lên: 07/08/2014, 06:22

... 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 combinatorics ... 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 g...

Ngày tải lên: 07/08/2014, 13:21

... heterochromatic matchings in edge- colored bipartite graphs, to appear in Ars Combinatoria, 2006. [15] H. Li and G.H. Wang, Color degree and heterochromatic matchings in edge- colored bipartite ... set of |T | distinct colors on some such set of |T | edges between S and distinct vertices of T . In [15], we obtained the following result concerning heterochromatic matchings...

Ngày tải lên: 07/08/2014, 21:21

... is 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. We use the ... all edges joining u j to U have color λ 2 , and all edges joining v j to V have color λ 1 . If U and V are both nonempty, then replacing u j v j with edges to each yields a larger ra...

Ngày tải lên: 08/08/2014, 11:20

... ,thenany point z j lies inside the triangle determined by the preceding three points in this ordering. To start the induction, for k =1wechoosez 1 to be a point, for k =2letz 1 and z 2 be any two distinct ... the distri- bution of longest increasing subsequences in random permutations, in preparation. [11] A. M. Odlyzko and E. M. Rains, On longest increasing subsequences in random per...

Ngày tải lên: 07/08/2014, 06:22