Báo cáo toán học: "An Inequality Related to Vizing’s Conjecture" docx

... ≤|D|, and the desired inequality (2) follows. References [1] Bert Hartnell and Douglas F. Rall, Domination in Cartesian Products: Vizing’s Conjecture, in Domination in Graphs—Advanced Topics edited by ... electronic journal of combinatorics 7 (2000), #N4 2 Theorem 1 For any graphs G and H, γ(G)γ(H) ≤ 2γ(G  H). Proof. Let D be a dominating set of G  H. It is sufficient to show that γ(G)γ...

Ngày tải lên: 07/08/2014, 06:20

... q-Identities related to overpartitions and divisor functions Amy M. Fu Center for Combinatorics, LPMC Nankai University, Tianjin 300071, P.R. China Email: ... K. Dilcher, Some q-series identities related to divisor functions, Discrete Math., 145(1995) 83–93. [5] A.M.FuandA.Lascoux,q-identities from Lagrange and Newton interpolation, Adv. Appl. Math., ... 25(1984) 377–379. [10] J. Zeng...

Ngày tải lên: 07/08/2014, 13:21

... Theor. Comput. Sci., 12(2):47–64, 2010. the electronic journal of combinatorics 18(2) (2011), #P18 7 Continued fractions related to (t, q)-tangents and variants Helmut Prodinger Department of Mathematics 7602 ... this continued fra ction expansions stops, since s r (z) = 0. Replacing z by −z we get zs 0 (−z) s −1 (−z) = z a 0 − z a 1 − z a 2 − z . . . . This translates into a continued fr...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 09:46

... contract to K 5 ,ands +3 colors are both necessary and sufficient to extend the coloring of G[P ]toallofG.The same construction, beginning with a copy of K 4 , creates a graph that does not contract to ... G. A. Dirac, Map colour theorems related to the Heawood color formula, J. London Math. Soc. 31 (1956), 460-471. [12] G. A. Dirac, Map colour theorems related to the Heawood colo...

Ngày tải lên: 07/08/2014, 07:21

... C B (p, q). Hence case (3.32) with respect to z is equivalent to case (3.31) with respect to z, and we have just shown this case to be impossible. Pictorially, z is obtained from z by swapping ... τ(i)isb i .Thei th row sum is equal to p i and the i th column sum is equal to q i . The weight of the board is equal to (σ), the sign of σ. An illustration of the board B 1 corresp...

Ngày tải lên: 07/08/2014, 08:20

... Now, the cops move to new positions. At this moment there is no cop in A, so the robber is able to move to any vertex of X in her turn; thus to complete the proof, we need to show that there ... larger than s. Proof. (i) To show connectivity one has to prove that every element of Z 1+k(s+1) 2 can be written as a linear combination of members of S, which is equivalent to the ma...

Ngày tải lên: 08/08/2014, 12:23

... vec- tors. Then, for any f 3 , . . . , f n−1 , Ψ( f 1 ) − Ψ(f 0 ), . . . , Ψ(f n−1 ) − Ψ(f 0 ) are linearly dependent. and λf = {(λx, µ) : (x, µ) ∈ f} where λ ∈ S. The linear space (X) is said to ... Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. An introduction to 2-fuzzy n-norme...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 10:20

... recurrence, it is necessary to understand why A i (q)=q i−1 C i−1 (q)C n−i (q). Since a path in A i first touches the diagonal at (i, i), it must go from (0, 1) to (i − 1,i) without touching the diagonal ... been shown to be C i−1 and thus have weight C i−1 (q). To these paths, we must add the i − 1 squares just above the diagonal from (0, 0) to (i, i). Thus the part of the paths fro...

Ngày tải lên: 07/08/2014, 06:22