Báo cáo toán học: "Perfect Matchings in Claw-free Cubic Graphs" pdf

... 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

... every claw-free cubic n-vertex graph with no cutedge has more than 2 n/12 perfect matchings, thus verifying the conjecture for claw-free graphs. 1 Introduction A gr aph is claw-free if it has no induced ... 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 comp...

Ngày tải lên: 08/08/2014, 14:22

... 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

... Theorem 1.2 and it serves as an introduction to it. We begin with a lemma about selecting induced forests of a particular kind in a bipartite graph. We introduce some terminology. Let H be a bipartite ... ··· ∪ M  induces a forest in G. We let T be the component of this forest containing the single vertex of M  . Since every vertex of M i−1 ,  < i ≤ k, has at least one neighbor in...

Ngày tải lên: 07/08/2014, 15:23

... [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

... 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

... 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

... questions, the most “interesting” subgraphs are the cycles. For this reason we consider only cycles in this paper. The girth of the graph is an interesting property which can be determined if enough ... other cycles whose length is in C. In fact, the resulting graph G 0 must be in R(m 1 , ,m t ). Let B denote the average number of ways to apply a backward r-switching to G 1 if G 1 is...

Ngày tải lên: 07/08/2014, 08:20

... vertices in graphs, IEEE Transactions on Information Theory, vol 44, pp. 599-611, 1998. [6] A. Lobstein, Bibliography on identifying and locating-dominating codes in graphs, http://www.infres.enst.fr/∼lobstein/debutBIBidetlocdom .pdf [7] ... minimal r-twin-free graph for the induced subgraph relationship. Indeed, we have: the electronic journal of combinatorics 15 (2008), #N17 5 An r-twi...

Ngày tải lên: 07/08/2014, 15:22