Báo cáo toán học: "Perfect matchings in -regular graphs" potx

... 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 each color class, at ... 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 a...

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 ... n < 2n 0 (d, g). 1 Introduction For a graph G, a 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...

Ngày tải lên: 07/08/2014, 13:21

... 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

... 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

... Thus, a 0-walk-regular graph is the same concept as a walk-regular graph. In the other ex- treme, the distance-regular g r aphs correspond to the case of D-walk-regular gr aphs (see e.g. Rowlinson [11]). ... paper we introduce a generalization of bo th distance-regularity and walk-regularity, which we call k-walk-regularity. In particular, we present some algebraic characterizations of k-...

Ngày tải lên: 07/08/2014, 21:21

... [2]). In [1], Biggs introduced perfect codes in graphs. From this point of view, a perfect binary single-error correcting code of length k is a perfect code on the hypercube Q k ,and a tiling of ... in nite length. Both existence and nonexistence results are given. 1 Introduction Perfect codes appeared in error correcting codes theory during the late 40’s with the work of Golay and Ham...

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

... 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

... 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