Báo cáo toán học: "The Minor Crossing Number of Graphs with an Excluded Minor" pot

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Ngày tải lên: 05/08/2014, 10:20

... 1–8. 4. W. Li, On the property of solutions of M-matrix equations, Systems Science and Math. S cience 10 (1997) 129–132. The Bounds on Comp onents of the Solution for Consistent Linear Systems ... a nonsingular M-matrix. Hence the result follows immediately from Theorem 3.1 of [3]. Vietnam Journal of Mathematics 33:1 (2005) 91–95 The Bounds on Componen...

Ngày tải lên: 06/08/2014, 05:20

... polyominoes. The area |c| of the polyomino c is the number of its unit squares. We denote by C n the set of all the polyominoes of area n. The perimeter P (c) of a polyomino c is the number of ... c 1 and c 2 . Putting these facts together, we see that for the values of n listed in the theorem, the sets of the minimal antecedents through the sequen...

Ngày tải lên: 07/08/2014, 06:20

... a construction for sets of integers with distinct subset sums Tom Bohman Department of Mathematics, 2-339 Massachusetts Institute of Technology 77 Massachusetts Ave. Cambridge, MA 02139 bohman@math.mit.edu Submitted: ... can make an approximation of L ≈ .22001865 with an error of less than 1.5 ·10 −7 . Inequality (10) can certainly be used to obtain more precise ap...

Ngày tải lên: 07/08/2014, 06:22

... 11−             =  c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8  the electronic journal of combinatorics 8 (2001), #R1 3 Hadamard matrices and strongly regular graphs with the 3-e.c. adjacency property Anthony Bonato Department of Mathematics, Wilfrid ... graphs are 3-e.c., the only known examples of strongly regular 3-e.c. graphs are Paley graphs with...

Ngày tải lên: 07/08/2014, 06:22

... 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

... z}∈H}. the electronic journal of combinatorics 10 (2003), #R18 2 The Turan Density of the Hypergraph {abc, ade, bde, cde} Zoltan Făuredi Department of Mathematics, University of Illinois Urbana, ... both F 3,2 and F 2,3 and they are different. The extremal graph problem of F 3,2 originates from a Ramsey-Tur´an hypergraph paper of Erd˝os and T. S´os [2]. Th...

Ngày tải lên: 07/08/2014, 07:21

... − 15 + 12 − 3=0 N char(dodecahedron) = 20 − 60 + 20 = −20 2 Computing the Neighborhood Characteristic The neighborhood characteristic of a graph can also be calculated in terms of the complete bipartite ... overcounting is corrected for in the following theorem (which also shows that, for a bipartite graph G, N char(G) equals twice the ‘bipartite characteristic defined in [5]). T...

Ngày tải lên: 07/08/2014, 07:21

... x]showsthats λ [s (1 a ,b) ][1 − x] = 0 unless λ is a hook. So we have shown that s [s à ]| hooks = 0 unless both and à are hooks, proving statement 1. If we now let λ =(1 c ,d), and for the ... is odd So statement 1 follows immediately by conjugating statement 1 of Theorem 4.5. When a is even, statement 6 follows by conjugating the formula in statement 6 of Theorem 4.5 and then subst...

Ngày tải lên: 07/08/2014, 08:20

... − Θ(1)) ≤ χ(NC n ) ≤ n(log 2 n−1). 1 Introduction Two sets are non-crossing if they are disjoint or one contains another. The non-crossing graph NC n is the graph whose vertex set is the set ... Published: Jan 25, 2006 Mathematics Subject Classifications: 05C88, 05C89 Abstract Two sets are non-crossing if they are disjoint or one contains the other. The non- crossing graph NC n is the...

Ngày tải lên: 07/08/2014, 13:21

... 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

... 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

... 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