Báo cáo toán học: "The Distinguishing Chromatic Number" pot

... for the independence number of general graphs of a given odd girth. We shall prove some similar bounds to those we prove for regular graphs in terms of a measure of the concentration of edges. Monien ... prove our results for graphs of odd girth at least 7. Dealing with graphs with larger odd girth will simply require a generalisation of this argument. Theo...

Ngày tải lên: 07/08/2014, 06:20

... Denley’s Theorem 4. References 1. Denley, T., The Independence number of graphs with large odd girth, The Electronic Journal of Combinatorics 1 (1994) #R9. 2 We can now prove the following theorem. Theorem ... is sharp for the regular complete bipartite graphs K aa . The above results are readily extended to graphs of larger odd girth. Lemma 2: Let G have odd girth...

Ngày tải lên: 07/08/2014, 06:20

... 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

... w) 2   The Fraction of Subspaces of GF(q) n with a Specified Number of Minimal Weight Vectors is Asymptotically Poisson Edward A. Bender Center for Communications Research 4320 Westerra Court San Diego, ... d-dimensional subspace of GF(q) n has the same number of ordered bases, the fraction of ordered bases with a desired property will be the same...

Ngày tải lên: 07/08/2014, 06:20

... the number of partitions of (the number) n,andQis its ordinary generating function. Also, define p(n, k) to be the number of partitions of n with largest part at most k. We will have use of the ... values of n, we shall use elementary estimates and some well-known bounds for ordinary partitions (of a number) to express most values of b n in terms of the number...

Ngày tải lên: 07/08/2014, 06:20

... point is a vertex. Such a drawing is said to be a rectilinear drawing of G.Therectilinear crossing number of G,denoted ν(G), is the fewest number of edge crossings attainable over all rectilinear ... rectilinear drawing of K n is a triangle. Prove that the convex hull of any optimal rectilinear drawing of K n is a triangle. 2. Given a rectilinear drawing...

Ngày tải lên: 07/08/2014, 06:22

... 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

... monotone subsequences of length 3 in L, R are also such subsequences of S.There are no monotone subsequences of S containing both 0 and n − 1. There are no monotone subsequences of S of the form a, ... up of k monotone descending subsequences, each of length n/k or n/k; clearly it has no monotone ascending subsequences of length k +1, and any monotone descendin...

Ngày tải lên: 07/08/2014, 07:21

... a 4 -distinguishing coloring. 3 Results for Trees In this section we prove two results about the distinguishing chromatic number of trees. We characterize those trees with distinguishing chromatic ... that is also r -distinguishing. 2 Preliminary Results In this section we present a table of results that shows the chromatic number, the distin- guishing number and the distinguishi...

Ngày tải lên: 07/08/2014, 13:21

... 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

... permutation of X. In this paper, we show that if G is nilpotent of class c or supersolvable of length c then G always acts with distinguishing number at most c + 1. We obtain that all metacyclic ... groups act with distinguishing number at most 3; these include all groups of squarefree order. We also prove that the distinguishing number of the action of the general lin...

Ngày tải lên: 07/08/2014, 13:21

... continuity that the chromatic polynomial has a root in the interval (1, 2). We can perform a similar analysis on the graphs obtained by adding the single edge v 1 v 4 to X(s, t) with the following ... an in nite family of 3-connected non-bipartite graphs with chromatic roots in the interval (1, 2) thus resolving a conjecture of Jackson’s in the negat...

Ngày tải lên: 07/08/2014, 13:21

... journal of combinatorics 15 (2008), #R4 11 The Minor Crossing Number of Graphs with an Excluded Minor Drago Bokal Department of Combinatorics and Optimization University of Waterloo Waterloo, Canada dbokal@uwaterloo.ca Gaˇsper ... Pinontoan and R. Bruce Richter. Crossing numbers of sequences of graphs. II. Planar tiles. J. Graph Theory, 42(4):332–341, 2003. [33...

Ngày tải lên: 07/08/2014, 15:22

... dense random graph. The notion of a t-stable set is a generalisation of the notion of a stable set. Recall that a set of vertices S of a graph G is stable if no two of its vertices are adjacent. ... graphs. Combinatorica, 11(1):45–54, 1991. [19] D. Matula and L. Kuˇcera. An expose-and-merge algorithm and the chromatic number of a random graph. In Random Graph...

Ngày tải lên: 08/08/2014, 12:22

... pebbling moves leading to a distibution with at least t pebbles at x. Answering a question of Sieben, we show that for every graph G, π t (G) is eventually linear in t; that is, there are numbers ... claim that, starting with p 0 , it is impossible to obtain t pebbles at x. To check this, we define the potential of a pebbling distribution p as F (p) :=  v∈V (G) p(v) mdist(v,...

Ngày tải lên: 08/08/2014, 14:23