Báo cáo toán học: "A LOWER BOUND FOR THE NUMBER OF EDGES IN A GRAPH CONTAINING NO TWO CYCLES OF THE SAME LENGTH" pptx

... critical reading of the manuscript and for pointing out a number of corrections. References [1] Chv´atal, V., Harary, F.: Generalized Ramsey theory for graphs. I. Diagonal numbers, Periodica Mathematica ... K km−1 of K n .A( C 2m ; n) k -coloring of K n is obtained by assigning the last color k to all remaining edges (See Fig. 2.) Indeed, on the contrary suppose that...

Ngày tải lên: 07/08/2014, 08:22

... determine the graphs with maximal or minimal Hosoya indices in a g iven class of graphs. As for n-vertex trees, it has been shown that the path has the maximal Hosoya index and the star has the minimal ... bound for the Hosoya index of do uble hexagonal chains. In [31], Shiu studied the extremal Hosoya index of hexagonal spiders. In light of the informati...

Ngày tải lên: 08/08/2014, 12:22

... v(G) 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 same length which leads to the following result. Theorem. ... Chunhui Lai, On the size of graphs with all cycle having distinct length, Discrete Math. 122(1993) 363-364. [6] Chunhui Lai, The edges in a graph...

Ngày tải lên: 07/08/2014, 06:22

... −1) matrix, M, below (so that there are t+ 1 instances of T in each row and in each column). We note that in the definitions of A and A  we have the color 0 present. This is valid since, as M ... defined in equation (1), the color 0 only occurs on the main diagonal of M and the main diagonal entries correspond to nonexistent edges in the complete graph. AB ...

Ngày tải lên: 07/08/2014, 06:23

... finite, non-oriented graphs without loops and multiple edges. We call a p-clique of the graph G asetofp vertices, each two of which are adjacent. The largest positive integer p, such that the graph ... for each i ∈{1, ,r}. The symbol G → (a 1 , ,a r ) means that there is no (a 1 , ,a r )-free coloring of the vertices of G. We consider for arbitrary natural...

Ngày tải lên: 07/08/2014, 13:21

...  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 avoids a ... 344 the electronic journal of combinatorics 6 (1999), #R3 6 [GG] R. Greenwood and A. Gleason, Combinatorial Relations and Chromatic Graphs,...

Ngày tải lên: 07/08/2014, 06:20

... leads to the points, among which the local maxima are to be found. Asking for the linear combination to have strictly positive coefficients (and not just nonnegative) assures that they are, in a ... constructions for the Heilbronn problem has two steps. First we use a computer implementation of simulated annealing (SA) to find a good configuration of points and then an a...

Ngày tải lên: 07/08/2014, 06:23

... study of pattern containment during his address to the SIAM meeting on Discrete Mathematics. Since then, there has been a great deal of published results on pattern containment that deal with pattern ... type of pattern known as layered patterns. Then in 2002, Albert, Atkinson, Handley, Holton & Stromquist (hereafter referred to as AAHHS) [1] determined a lower bound fo...

Ngày tải lên: 07/08/2014, 15:23

... out the theoretical proof and drafted the manuscript. XH participated in the design and coordination. Both of the two authors read and approved the final manuscript. References [1] Liapunov, AM: ... your research in Journal of Inequalities and Applications go to http://www.journalofinequalitiesandapplications.com/authors/instructions/ For information about other SpringerO...

Ngày tải lên: 20/06/2014, 21:20

... solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping in Banach spaces. Ibaraki and Taka- hashi [10] introduced a new resolvent of a maximal monotone ... operator in Banach spaces and the concept of the generalized nonexpansive mapping in Banach spaces. Honda et al. [11], Kohsaka and Takahashi [12] also studied some pr...

Ngày tải lên: 20/06/2014, 21:20