Báo cáo toán học: "Independence number of 2-factor-plus-triangles graphs" pot

... The Number of Solutions of X 2 =0 in Triangular Matrices Over GF(q) Shalosh B. EKHAD 1 and Doron ZEILBERGER 1 Abstract: We prove an explicit formula for the number of n ì n upper triangular matrices, ... matrix, is given by the polynomial C n (q), where, C 2n (q )=  j  2n n − 3j  −  2n n − 3j − 1  · q n 2 −3j 2 −j , C 2n+1 (q )=  j  2n +1 n − 3...

Ngày tải lên: 07/08/2014, 06:20

... 1. ProofofTheorem3: Let a(G) be the number of automorphisms of an unlabeled n-vertex graph G. The number of distinct labelings of G is n!/a(G). If f (·)isa statistic on graphs, its expectation on labeled ... the proofofTheorem1. 1.9 1.92 1.94 1.96 1.98 2 2.02 2.04 0 0.2 0.4 0.6 0.8 1 t Figure 2: The plot of à (t) for 0 t ≤ 1. 4 Proof of Theorems 2 and 3 Proof of Theorem 2...

Ngày tải lên: 07/08/2014, 07:21

... when p divides m − n, all permutation binomials occur in pairs over F 4p+ 1 where p and 4p +1 areprimes. Theorem 12 Let q = 4p + 1where p and q are primes. The following are paired permu- tation binomials ... (3) If 3p& lt;m< 4p then (mod 4) m ≡ 1 m ≡ 2 m ≡ 3 m ≡ 4 p ≡ 1 2 (p − 1) + N 1 + N 2 2N 1 2 (p − 1) + N 1 + N...

Ngày tải lên: 07/08/2014, 13:21

... The number of 0-1-2 increasing trees as two different evaluations of the Tutte polynomial of a complete graph C. Merino ∗ Instituto de Matem´aticas, Universidad Nacional Aut´onoma de M´exico, Circuito ... present an algebraic proof of a result with the same flavour as the latter: T n+2 (1, −1) = T n (2, −1), where T n (1, −1) has the combinatorial i...

Ngày tải lên: 07/08/2014, 15:22

... z 3/2 g w 1 + z 3/2 h w 1 + z 2 j w 1 ) (46) g w AZ w = P w AZ w AZ w 1 (z 1/2 P w 1 + zh w 1 ) (47) h w AZ w = P w AZ w AZ w 1 (z 1/2 P w 1 + zg w 1 ) (48) j w AZ w = P w 1 AZ w 1 + g w AZ w AZ w 1 (z 1/2 P w 1 + ... with (1, −1), then there could be an arbitrary [00] walk with width w − 1 in between. If the walk starts with (1, 1) and ends wit...

Ngày tải lên: 07/08/2014, 15:22

... in J. Graph Theory. the electronic journal of combinatorics 15 (2008), #R82 9 Irregularity strength of regular graphs Jakub Przybylo AGH University of Science and Technology Al. Mickiewicza ... of G is a map f : E(G) → {1, 2, . . . , w}. An irregularity strength of G, s(G), is the smallest w such that there is a w-weighting of G for which  e:u∈e f(e) =  e:v∈e f(e) for a...

Ngày tải lên: 07/08/2014, 21:20

... Hence, the class of (maximal) planar graphs is contained in the class of maximal K 3,3 -minor-free graphs and we can use the number of planar graphs and the number of triangulations as lower bounds. ... preliminary version available at http://algo.inria.fr/flajolet/Publications [7] O. Gim´enez and M. Noy. The number of planar graphs and properties of random planar...

Ngày tải lên: 07/08/2014, 21:20

... Press, 1987. the electronic journal of combinatorics 16 (2009), #N32 6 Skew Spectra of Oriented Graphs Bryan Shader Department of Mathematics University of Wyoming, Laramie, WY 82071-3036, USA email: ... σ. Proof. (Necessity) See the proof of Theorem 3.3 in [1]. (Sufficiency) Suppose Sp S (G σ ) = iSp(G) for any orientation σ. By Theorem 2.2, G is a bipartite graph. And so there...

Ngày tải lên: 07/08/2014, 21:21

... set of q edges with weight at least s in a graph G. If the total weight of edges in Q is at most cq, then rep(L(G)) ≥ max k>s 2(k−c) (k−s)(k−s+1) q. Proof. Let X i be the number of edges of ... define the repetition number of a graph G, written rep(G), to be the maximum multiplicity in the list of vertex degrees. We study the minimum of rep(G) on various classes of n-ver...

Ngày tải lên: 07/08/2014, 21:21

... “intersection graph” of the components in G 1 and G 2 ). By construction, H is bipartite. The degree of a vertex in H is the number of vertices in the corresponding component of G 1 or G 2 . Each edge of H corresponds ... {a ∈ A: a /∈ B}. 2 Independence ratio at least 1/4 The independence number of a graph is the sum of the independence numbers of its components. Therefore...

Ngày tải lên: 07/08/2014, 21:21

... between the mutation class of a quiver of type D n and triangulations up to rotation and inverting tags Here we adapt the methods and ideas of [T] to obtain a bijection between the mutation class of ... 1: The mutation class of D 4 . It is know from [FZ3] that the mutation class of a Dynkin quiver Q is finite. An explicit formula for the num...

Ngày tải lên: 07/08/2014, 21:21

... distinguishing number two. the electronic journal of combinatorics 17 (2010), #R20 6 Distinguishing Number of Countable Homogeneous Relational Structures C. Laflamme ∗ University of Calgary Department of ... skeleton of a structure A is the set of finite induced substructures of A and the age of A consists of all relational structures isomorphic to an element of...

Ngày tải lên: 08/08/2014, 11:20

... words Every binary word with at least 4 letters co ntains a square. A. S. Fraenkel and J. Simp- son [2, 1] studied the number of distinct squares in binary word; see also Ilie [4], where it was shown that ... no words in this list of length 29. the electronic journal of combinatorics 18 (2011), #P6 7 The Number of Positions Starting a Square in Binary Word...

Ngày tải lên: 08/08/2014, 12:23

... matchings are special cases of F -matchings. Let F and G be graphs. An F -matching in G is a subgraph o f G consisting of pairwise vertex disjoint copies of F . We say that the F -matching is ... set of F -matchings not covering v being a separate cla ss C 0 . We argue that the number of F -matchings in each such class is a zero residue...

Ngày tải lên: 08/08/2014, 12:23

... types of the independence complexes of some stable Kneser graphs are already known. For n = 1, the stable Kneser graphs are complete graphs and thus their independence complexes are wedges of 0-dimensional ... at the homotopy type of the indep en dence complex of SG 2,k is a wedge of spheres of dimension two. Second, we determine the homotopy types of the independe...

Ngày tải lên: 08/08/2014, 14:23