Báo cáo toán học: "Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size" doc

... number of vertices from the hub. the electronic journal of combinatorics 13 (2006), #R29 4 Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size Ronald Gould Department of Mathematics ... showed for l ≥ 5thatsat(n, C l ) ≥ n  1+ 1 2l+8  . We will provide an upper bound for the function sat(n, C l ) that improves the upper bound given in [1] for m...

Ngày tải lên: 07/08/2014, 13:21

... is known, otherwise upper and lower bounds for γ(n, δ). We establish these values in Sections 2, 3 and 4. TIGHT UPPER BOUNDS FOR THE DOMINATION NUMBERS OF GRAPHS WITH GIVEN ORDER AND MINIMUM DEGREE W. ... uneven distribution of degree for the vertices of a graph leads to a higher value of γ even though the number of vertices and the number of edges remains the sa...

Ngày tải lên: 07/08/2014, 06:20

... approximations of the roots for specific values of d are found easily, and so are the inverses of the roots of smallest modulus giving us the entries of first line of table 2. the electronic journal of combinatorics ... 05A15 Abstract New upper bounds for the connective constant of self-avoiding walks in a hypercubic lattice are obtained by automatic generation of finit...

Ngày tải lên: 07/08/2014, 06:20

... entry in the table of values of γ(n, δ)in[2] Acknowledgement We wish to thank Gordon Royle for providing Cayley tables for the 14 groups of order 16 and Cayley graphs of groups of orders up to 31. References [1] ... group of order 16 with δ =10andγ =3 the electronic journal of combinatorics 7 (2000), #R58 19 [2] W. Edwin Clark and Larry A. Dunning, Tight Upper Bounds...

Ngày tải lên: 07/08/2014, 06:22

... 106314989 µ(14, 8) 12312902 17297280 Table 2: Upper bounds for µ(n, d) obtained by µ(n, d)  nµ(n − 1, d) Proof. For each i, a i |C| counts the number of pairs of permutations (φ, ψ) with φ, ψ ∈ C and ... [15], many of the upper bounds obtained by linear pro- gramming coincide with the bound µ(n, d)  n! (d−1)! of theorem 1. For 14  n  16, computations of the LP boun...

Ngày tải lên: 08/08/2014, 12:22

... new and sharp upper bounds for λ(G), which are better than all of the above mentioned upper bounds in some sense, and determine the extremal g r aphs which achieve these upper bounds. Some examples ... paper, we present three improved upper bounds for the Laplacian spectral radius of graphs. Moreover, we determine all extremal graphs which achieve these upper boun...

Ngày tải lên: 08/08/2014, 12:23

... construct families of (k, g) -graphs from those of k-regular graphs of girth at least g. Applying this construction to the graphs CD(2 g+1 2  − 5, q), we obtained the upper bounds given in (3) ... v(k,g)≥ k(k−1) (g−1)/2 −2 k−2 for g odd, and v(k,g)≥ 2(k−1) g/2 −2 k−2 for g even. The best known upper bounds are roughly the squares of the lower bounds. In this paper...

Ngày tải lên: 07/08/2014, 06:22

... New upper bound for a class of vertex Folkman numbers N. Kolev Department of Algebra Faculty of Mathematics and Informatics “St. Kl. Ohridski” University of Sofia 5 J. Bourchier ... 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 t...

Ngày tải lên: 07/08/2014, 13:21

... density of a permutation pattern π is the limiting value, n → ∞, of the maximum proportion of subsequences of σ ∈ S n that are order-isomorphic to π. We generalize methods for obtaining lower bounds ... = |σ T |) of choosing m points from σ T that form a π-pattern. One way for this to occur is when all of the selected m points of the π-pattern lie in a single σ t i . The p...

Ngày tải lên: 07/08/2014, 15:23

... orbit of C under Aut(G) ×S n corresponds to the type of L(C). Therefore the number of non-isomorphic edge-colourings of G is the number of types of Latin squares of order n. A one-fac tor of a ... subgraph. A de- composition of G is a set of subgraphs of G whose edge sets partition the edge set of G. In particular, a one-factorisation of G is a decomposition of G i...

Ngày tải lên: 08/08/2014, 01:20