Báo cáo toán hoc:" Rainbow matchings in r-partite r-graphs" pps

... 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 ... matching is said to be s -rainbow. If M has an earmarking φ such that |Im(φ)|  s we say also about M by itself that it is s -rainbow. In this article we study matchings in r-parti...

Ngày tải lên: 08/08/2014, 01:20

... is called 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 ... 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]...

Ngày tải lên: 08/08/2014, 14:23

... 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 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

... 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 in colored bipartite ... 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 edg...

Ngày tải lên: 07/08/2014, 21:21

... 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 ... n 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-colore...

Ngày tải lên: 08/08/2014, 11:20

... 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

... 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

... surfaces. Interdiscip. Inf. Sci., 12(2):93–107, 2006. the electronic journal of combinatorics 15 (2008), #N11 5 Lattice points in Minkowski sums Christian Haase, Benjamin Nill, Andreas Paffenholz ∗ Institut ... a (closed) strip R of lattice width one. The interior of R intersects precisely two edges of Q, since the strip contains no lattice point in its interior. Those two are the only edg...

Ngày tải lên: 07/08/2014, 15:23

... coefficients in F q 2 , up to a nonzero scalar. Again, since the point P ∞ is an o rdinary triple point for Γ and since C 3 is absolutely irreducible, we get that P ∞ is a simple point of either ... through the point P ∞ , where C n has order n for some 1 ≤ n ≤ 5. Case n = 1 Suppose first that there exists a line ℓ of P G(2, F) contained in Γ and passing through the point P ∞ . Since ℓ is a...

Ngày tải lên: 07/08/2014, 21:21