Báo cáo toán học: "R(3, 4) = 17" ppt

... the theories of matroids with coecients and of -matroids with coecients, Beitrăage zur Algebra und Geometrie 37 (1996), 161-198. [682] W. Wenzel: Projective equivalence of ∆ -matroids with coefficients ... W. Wenzel: Projective equivalence of matroids with coefficients, J. Combinatorial Theory, Ser. A 57 (1991), 15-45. [680] W. Wenzel: Combinatorial Algebra of ∆ -Matroids and Related Combi...

Ngày tải lên: 07/08/2014, 05:23

... generate random matchings rather than merely count them, then, given a random bit, a random matching in the before graph is readily transformed into a random matching in the after graph, and conversely, ... v 1 and v 2 of G are connected by an edge, and that f is a face bounded by this edge. The height difference between the diagonal from v 1 to f and the diagonal from v 2 to f is dete...

Ngày tải lên: 07/08/2014, 06:20

... the same class. In general, a poset realizes two graphs simultaneously: one is its upper bound graph and another, its lower bound graph. These graphs may be thought of as two meanings of the poset, ... characterization of upper bound graphs, Congr. Numer. 40 (1983), 189–193. [6] J. R. Lundgren, J. S. Maybee, and F. R. McMorris, Two -graph inversion of competition graphs and upper bound gr...

Ngày tải lên: 07/08/2014, 06:20

... that the existence of a 4-cycle system of order n having an m-colouring of type bd, implies the one of a 4-cycle system of order n + 8 having an (m + 1)-colouring of type bd. ✷ 4 2-Colouring of ... , n+3 4 } there is a 4-cycle system of order n with a proper m-colouring of type bf . Proof.Thecasesm =3andm = n+3 4 are proved by using Theorem 2.3 and Theorem 2.4 re...

Ngày tải lên: 07/08/2014, 06:22

... yields the result via Lemma 3.1. 4 Not strongly connected subgraphs In this section we turn our attention to ∆ NSC G , the complex of subgraphs of G that are not strongly connected. More precisely, ∆ NSC G = ... partitions into strongly connected components of subgraphs of G. The partition corresponding to the electronic journal of combinatorics 11 (2004), #R75 4 Directed subgraph complexe...

Ngày tải lên: 07/08/2014, 08:22

... symmetries. For example, the Wilf classes for single permutations of length 4, 5, 6, and 7 are known. There are, up to symmetry, 56 classes of pairs of permutations of length four. Numer- ical data ... argument along the lines of the one above for Case 2 [Figure 12c]. the electronic journal of combinatorics 12 (2005), #R25 15 Wilf classes of pairs of permut...

Ngày tải lên: 07/08/2014, 08:22

Ngày tải lên: 07/08/2014, 13:21

... for total 4-choosability, and it completes the proof of Lemma 8. ✷ Lemma 9. If a nontrivial sepachain G 1 is good for total 4-choosability, then so is the sepachain G in Fig. 1(h). Proof. Let Λ ... Λ-colouring of G, and this completes the proof of Lemma 5. ✷ Lemma 6. If a nontrivial sepachain G 1 is good for total 4-choosability, then the sepachain G in Fig. 1(f) is very good for tot...

Ngày tải lên: 07/08/2014, 13:21

... 2) difference sets to construct images (96, 20, 4) difference sets in groups of order 32 and then used those images to construct (96, 20, 4) difference sets in GAP[96,221] and GAP[96,231]. The difference ... (96, 20, 4) difference sets in some 72 groups groups of order 96, those groups that have both factor groups of order 32 and 24. Table 1 lists...

Ngày tải lên: 07/08/2014, 15:22

... 4.2. lim k→∞  R(k,k) 2  R R(k,k) (k, k) = c < ∞ It follows from Theorem 2.1 that R(4, 4) ≤ 36 by considering the game on n(4, 4) = 2n(3, 4) = 20 vertices. But, since 9 = R(3, 4) < n(3, 4) = 10, one can expect ... the Book. Theorem 3.2. R(3, 4) = 17 Proof. Since R(3, 4) ≤ R 12 (3, 4) = 17 (see Theorem 3.1) it is enough to show that R(3, 4)...

Ngày tải lên: 07/08/2014, 15:23

... a graph G is circular q 1 -degree- choosable if and only if G is circular q 2 -degree- choosable. We say that a graph is circular degree- choosable if it is circular q -degree- choosable for some ... that l 1 (v) = deg(v). So a graph is circular 1 -degree- choosable if and only if it is degree- choosable. In the following, we only consider circular q -degree- choosability for q ≥ 2. We w...

Ngày tải lên: 07/08/2014, 21:20

... bijection between the set of vertices of G and the set of vertices of H. We now show that given any pair a, b of vertices of G (which might also coincide), the set E(a, b) of edges between these ... journal of combinatorics 16 (2009), #N6 1 of f(a) and thus the 3ε-neighborhood of f (a) is a simple arc (lying in the interior of some edge) in H. Consider the points a 1 ,...

Ngày tải lên: 07/08/2014, 21:21

... of a cubic lattice, then there are 35 different incidence symbols for labeled {4, 5} sponges that lead to exactly 15 different geometric {4, 5} sponges. The 15 unlabeled geometric {4, 5} sponges ... symmetry of the whole polyhedron. This is the definition of an isogonal polyhedron. One can hazard to guess that the ancients had the former meaning in mind, whil...

Ngày tải lên: 07/08/2014, 21:21

... Laplacian spectrum of weakly quasi -threshold graphs, Graphs and Combinatorics, to appear. [2] H. Christianson and V. Reiner, The critical group of a threshold graph, Linear and its Applications 349 ... graph in terms of the number of cutpoints, Linear and Multilinear Algebra 47 (2000), 93-1 03. [8] S. Kirkland, Constructably Laplacian Integral Graphs, Linear Algebra and its Appli- cations...

Ngày tải lên: 07/08/2014, 21:21

... Similarly, an abelian r’th power is a concatenation of r blocks, each of length n, where each block is a permutation of the first n symbols. For example, deeded is an abelian cube. Abelian squares ... counting abelian powers. We discuss enumerating the abelian squares over an alphabet of size k and give an a symptotic estimate for this quantity. 2 Preliminaries Let f k (n) be the num...

Ngày tải lên: 07/08/2014, 21:21