Báo cáo toán học: "Repetition number of 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

... the class of all 4-chromatic graphs. The structure of the red graph is obvious by Corollary, but we do not know which graphs can occur as blue graphs and what are the properties of graphs in which ... on the Wall, a list of conjectures of Graffiti. Ramseyan Properties of Graphs by Ermelinda DeLaVina delavina@math.uh.edu Siemion Fajtlowicz siemion@math.uh.edu Uni...

Ngày tải lên: 07/08/2014, 06:20

... The notion of orthogonal colorings is strongly related to the notion of orthogonal Latin squares. The orthogonal chromatic number of G, denoted by Oχ(G), is the minimum possible number of colors ... 2, 3, 1, 3). The notion of k -orthogonal colorings is strongly related to the notion of orthogonal Latin squares. Recall that two Latin squares L 1 ,L 2 of order r are...

Ngày tải lên: 07/08/2014, 06:20

... parts are all of size one. Alternately, the complement of such a graph either has no edges or consists of the the disjoint union of three or fewer complete graphs. Proof. The complement of K − 5 is ... similar proofs for complexes of dimension 2 and higher. We conjecture that the answer is “yes,” but the complexity of the proof would be astronomical, even for dimension 2. Hidden...

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

... 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

... 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

... the transposition of the remaining two vertices. This implies that the only graphs which have fix(G) = n−1 are the complete graphs and the empty graphs. On the other hand, the graphs with fix(G) ... e), where v and e are a vertex and an edge of G, and v and e are incident. Inf(G) has an edge between (v 1 , e 1 ) and (v 2 , e 2 ) if v 1 = v 2 or e 1 = e 2 . We denote the...

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

... electronic journal of combinatorics 16 (2009), #R92 2 Defective choosability of graphs without small minors Rupert G. Woo d and Douglas R. Woodall School of Mathematical Sciences, University of Nottingham, Nottingham ... and S. Hedetniemi, Graphs with forbidden subgraphs. J. Combin. Theory Ser. B 10 (1971) 12–41. [3] G. A. Dirac, A property of 4-chromatic graphs and s...

Ngày tải lên: 08/08/2014, 01:20

... 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