Báo cáo toán học: "Heterochromatic matchings in edge-colored graphs" potx

... 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 of such matchings ... 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 ea...

Ngày tải lên: 07/08/2014, 06:22

... The 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

... 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

... 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 have ap...

Ngày tải lên: 08/08/2014, 01:20

... e 3 will be incident with v 1 , v 2 , v 3 respectively. Every ver tex in a claw-free cubic graph is in 1, 2, or 3 triangles. If a vertex is in 3 triangles, then the component containing the vertex ... permanents of certain (0, 1)-matrices. Nederl. Aka d. Wetensch. Ind ag. Math., 41(1):83– 86, 1979. the electronic journal of combinatorics 18 (2011), #P62 6 Perfect Matchings in Claw-f...

Ngày tải lên: 08/08/2014, 14:22

... 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 ... then G has a rainbow matchin g of size at least ⌊ 2δ 3 ⌋. Keywords: rainbow matchings, properly colored graphs, triangle-free graphs 1 Introduction and notation We use [3] for termin...

Ngày tải lên: 08/08/2014, 14:23

... t). A join pair (G, t) is a join covered pair if each edge of G lies in a minimum t-join. Note that if T is a t-join in a join pair (G, t) and C is a circuit with more than half its edges in T , ... 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...

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 ... ≥−1. Using the fact that K is a minimal cut set, by Hall’s Theorem (see for instance [2]) there is a matching of K into L and respectively K into R, which together produce k + t pa...

Ngày tải lên: 07/08/2014, 07:21

... 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