Báo cáo toán học: "Digraphs are 2-weight choosable" ppt

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Ngày tải lên: 05/08/2014, 10:20

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Ngày tải lên: 05/08/2014, 15:21

... ,q n . Then the subset sums are equidistributed modulo m if and only if h(q) is divisible by (q m − 1)/(q −1). Proof. First, for each i =0, 1, 2, ,leta i be the number of these sums that are equal ... 20 22 24 26 28 30 Figure 1. Dots indicate that t -subset sums from [n] are equidistributed modulo m.Byfixingm and varying t and n, various patterns are revealed. For exam...

Ngày tải lên: 07/08/2014, 06:20

... and φ cannot be distinguishing. This contradicts our assumption that φ is an r-distinguishing labeling. ✷ We remark that this proves that the largest integer in D(S 3 )is3,since the subgroups ... the goal is to minimize the number of colors used. Consequently we define the distinguishing number of a graph G by D(G)=min{r | G has a labeling that is r-distinguishing}. The original key problem...

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

... examine only bicolorings of Steiner triple systems. A coloring ϕ of D is a bicoloring if for all B ∈B,|ϕ(B)|=2,where ϕ(B)=∪ v∈B ϕ(v). This definition implies that in a triple system every triple has two elements ... Upper chromatic number of Steiner triple and quadruple systems, Discrete Math. 174 (1997), 247-259. [6] L. Milazzo, Zs. Tuza, Strict colourings for classes of Steiner...

Ngày tải lên: 07/08/2014, 06:20

... realtime random greedy algorithm.Welettimetgo continuously starting from zero. The packing P = P t will vary with time as will S t = V −  P t .WeletH t denote the restriction of H to S t .Ifbytimetedge ... idea that the revival of w at time s makesrevivalsat later times less likely as it lowers the degree. More formally, as X s ≥ deg s (w) the probability w is revived at time s is at m...

Ngày tải lên: 07/08/2014, 06:22

... Kalbfleisch. Chromatic Graphs and Ramsey s Theorem. Ph.D. Thesis. University of Waterloo, January, 1966. [3] K. Piwakowski. Applying Tabu Search to Determine New Ramsey Graphs. Electronic J. Combinatorics. ... 19, 1998; Accepted: May 14, 1998. Abstract New lower bounds for 15 classical Ramsey numbers are established. Several of the colorings are found using a new variation of local...

Ngày tải lên: 07/08/2014, 06:22

... (10) Sylvester treated the Euclidean division by a different method, using summations on subsets of roots (cf. [LP]). We shall for our part interpret now the Euclidean division as producing a sequence ... )=det  S λ i +j−i ( − )  1≤i,j≤ . Then Theorem 1 The k-th remainder in the Euclidean division of σ z ( ) by 1 is f k (z)=S (k+1) k ( ) −1 ∞  i=0 z i S k+1+i,(k+1) k−1 ( ) . (6)...

Ngày tải lên: 07/08/2014, 06:22

... squarefree word, i.e. an infinite sequence not containing any squares. Variations on the problem of finding squarefree words have included finding infinite squarefree tilings [2], or finding infinite ... There are ternary circular square-free words of length n for n ≥ 18. James D. Currie ∗ Department of Mathematics and Statistics University of Winnipeg Winnipeg, Mani...

Ngày tải lên: 07/08/2014, 06:23

... diameter of a recursively directed hypercube that is defined by a set of orientation functions with arities bounded by a constant k? 5 Summary In this paper we presented recursively directed hypercubes, ... but the diameter of a recursively directed hypercube may be exponential in n. Finally, we presented an an open question in respect to a diameter of a subclass of recursively...

Ngày tải lên: 07/08/2014, 06:23

... 3 Generalized patterns Here we consider packing generalized patterns into words. Generalized patterns were introduced by Babson and Steingr´ımsson [2] ... occurrences of patterns in Π (Π -patterns, for short) in a string σ. the electronic journal of combinatorics 9(2) (2003), #R20 4 with monotone and layered patterns in Section 2, with generalized patterns ... from permutations...

Ngày tải lên: 07/08/2014, 07:21

... 5, 6, 7} 8 1 2 5 14 {0, 1, 2, 3, 4, 5, 6, 7} 64 1 2 5 14 Table 5: Classifying S 7 by subsequence containment by involutions. the electronic journal of combinatorics 12 (2005), #R14 9 Before ... 5} 2 1 2 4 11 31 102 {0, 1, 2, 3, 4, 5} 16 1 2 5 14 43 142 Table 3: Classifying S 5 by subsequence containment by involutions. J (τ) |{τ}| I 6 (τ) I 7 (τ) I 8 (τ) I 9 (τ) I 10 (τ) {0, 1, 2...

Ngày tải lên: 07/08/2014, 08:22

... point, there must then be some point x common to all three lines. Fix a point x of the geometry. Now, each point is incident to m + 1 lines, so the probability that three or more points contain x ... that lines that contain q + 2 or more points are forbidden, although lines that containt q + 1 points are possible. The class L(q) adheres to other restrictions that elude our present interest, ....

Ngày tải lên: 07/08/2014, 13:21

... nonzero. The 2-weight choosability of digraphs not only solves the problem of 2-weight coloura- bility of digraphs (Problem 2), but it also yields the following interesting results which are not, ... isolated edge is 3-weight choosable. Regarding digraphs, it is shown in [BGN09] that all digraphs are 2-weight choosable, thus completely solving Problem 2. However, as their proof was...

Ngày tải lên: 08/08/2014, 12:23