Báo cáo toán học: "Sharp lower bound for the total number of matchings of tricyclic graphs" doc

... T n be the class of tricyclic graphs on n vertices. In this paper, a sharp lower bound for the total number of matchings of graphs in T n is determined. 1 Introduction The total number of matchings ... index of hexagonal spiders. In light of the information available for the total number of matchings of trees, unicyclic graphs, bicyclic gr...

Ngày tải lên: 08/08/2014, 12:22

... 1. Then f(n) ≥ n +32t − 1, for n ≥ n t . This completes the proof of the theorem. From the above theorem, we have lim inf n→∞ f(n) − n √ n ≥  2+ 2562 6911 , which is better than the previous bounds √ 2(see[2]),  2+ 487 1381 (see ... denote the number of vertices, and (G) denote the number of edges. In this paper, we construct a graph G having no two cycles with the...

Ngày tải lên: 07/08/2014, 06:22

... 1994 Abstract For k ≥ 5, we establish new lower bounds on the Schur numbers S(k) and on the k-color Ramsey numbers of K 3 . For integers m and n ,let[ m, n ]denotetheset{ i | m ≤ i ≤ n }.AsetSof integers ... [4] and the upper bound in [6]. For Ramsey numbers we know R 2 (3) = 6 and R 3 (3) = 17; the current bounds on R 4 (3) are 51 and 65 [5]. Below we list the five sets...

Ngày tải lên: 07/08/2014, 06:20

... color the edges of the complete graph on n vertices with k colors then there is always a monochromatic copy of G i colored with i,forsome1≤ i ≤ k. Wegivealower bound for k−color Ramsey number ... 1 vertices. the electronic journal of combinatorics 12 (2005), #N13 2 New lower bound for multicolor Ramsey numbers for even cycles Tomasz Dzido ∗ Institute of Mathematics...

Ngày tải lên: 07/08/2014, 08:22

... Then |E(G)|≤  k−2 2 + 1 k−1  |V(G)|−1. (1) The second ingredient of our proof is the following result of Stiebitz. Lemma 3 ([5]) Let G be a k-critical graph containing at least one vertex of degree k − 1. Then the number of connected ... components of its high-vertex subgraph H(G) does not exceed the number of connected components of its low-vertex subgraph L(G). P...

Ngày tải lên: 07/08/2014, 06:22

... arguments will hold for the 4-cycle C v ). The degree of the vertices a, b and c in G ′ and G remain unchanged. By Claim L, x u is adjacent to at least two of the vertices a, b and c (for otherwise, C u would ... N(v). For a set S of vertices, the open neighbor hood of S is defined by N(S) = ∪ v∈S N(v), and the closed neighborhood of S by N[S] = N(S)∪S. If X, Y ⊆ V ,...

Ngày tải lên: 08/08/2014, 12:23

... Classification: 05D10 Abstract We give two lower bound formulas for multicolored Ramsey numbers. These formu- las improve the bounds for several small multicolored Ramsey numbers. 1. INTRODUCTION In this ... k 1 +1,k 3 , ,k r ) − 1). Before giving the proof of this theorem, we have need of the following definition. the electronic journal of combinatorics 9 (2002), #R13 2 E...

Ngày tải lên: 07/08/2014, 06:23

...  rtimes )≥4(6.48) r−1 +1 holds for all r.ForR(6, 6, 6) there was no established nontrivial lower bound. Consider the number R(5, 5, 5). To find a lower bound, L, we are searching for a three coloring of K L which ... the result of this section to R(3, 3, 3, 4) and using the fact that R(3, 3, 4) ≥ 30 [K], we get the new lower bound: R(3, 3, 3, 4) ≥ 91. Using the...

Ngày tải lên: 07/08/2014, 06:20

... stationary points of f, see [5] for more details. The fulfilment of this condition together with the context of the situation serves to characterise the local maxima of f. As an illustration of the local ... with area log n/n 2 for every fixed n; lower bounds on higher dimensional versions of the problem, produced in 1999 by G. Barequet [2] and the study of th...

Ngày tải lên: 07/08/2014, 06:23

... have cl(G i )=a i − 1 for i =1, 2. (14) From (13), (14) and Lemma 1 we conclude that The number of the vertices of each connected component of ¯ G 1 is an even number; (15) and the number of the vertices of exactly ... overview of the results about the numbers F (a 1 , ,a r ; m − 1) was given in [1]. Here we shall note only the general bounds for the numb...

Ngày tải lên: 07/08/2014, 13:21