Báo cáo toán học: "A note on K∆+1-free precolouring with ∆ colours Tom Rackham" doc

... note on the almost sure limit theorem for self-normalized partial sums of random variables in the domain of attraction of the normal law Qunying Wu 1,2 1 College of Science, Guilin University of ... sequence of independent and identically distributed random variables in the domain of attraction of a normal distribution. A...

Ngày tải lên: 20/06/2014, 21:20

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Ngày tải lên: 05/08/2014, 10:20

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Ngày tải lên: 05/08/2014, 15:20

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Ngày tải lên: 05/08/2014, 15:21

... any nonhamiltonian Burkard–Hammer graph is contained in a maximal nonhamil- tonian Burkard–Hammer graph. So knowledge about maximal nonhamiltonian Burkard–Hammer graphs provides us certain information about nonhamiltonian Burkard–Hammer ... assume that all con- sidered in this paper maximal nonhamiltonian Burkard–Hammer graphs G = S(I ∪ K, E)haveδ(G)=|I|−k where |I|≥k...

Ngày tải lên: 06/08/2014, 05:20

... need only show that no prefix of m n is an overlap. First note that no prefix of m n is a square of length 12 or greater; otherwise the prefix of m n of length 6 reappears internally, i.e. m n contains ... m j , a contradiction since m j is overlap-free. Since aab is a prefix of m i ,f(aab)=aaf(b)isaprefixofm j . However, another prefix of m j is aabaab. Thus one of f (b)andbaab i...

Ngày tải lên: 07/08/2014, 06:20

... the reflection representation of a finite Coxeter group. This is essentially what we are looking at. (The defining representation of S n consists of the direct sum of the reflection representation ... have: Proposition 1.2. dim F n = D(n). Proof. Consider the table of the characters χ N ; we are interested in the dimension of the row-span of this table. Since t...

Ngày tải lên: 07/08/2014, 06:20

... A Note on Sparse Random Graphs and Cover Graphs ∗ Tom Bohman † Alan Frieze ‡ Mikl´os Ruszinko Đ Lubos Thoma ả Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, ... a constant κ<2/3, then it outputs a cover graph whp. Note that the output graph will have whp girth equal to 4. On a related note we point to [8] which surveys constructions of no...

Ngày tải lên: 07/08/2014, 06:20

... sharp estimates obtained by Kamath et al. of the probability that no bin is empty after the random placement of the balls and exploiting the relationship between the placement of balls and the rigid ... A note on the non-colorability threshold of a random graph Alexis C. Kaporis, Lefteris M. Kirousis, and Yannis C. Stamatiou University of Patras Departm...

Ngày tải lên: 07/08/2014, 06:20

... is (k, )-sum-free for k,  ∈ N, k>,ifthere are no solutions to the equation x 1 + ···+ x k = y 1 + ···+ y  in A. Denote by SF n k, the number of (k, )-sum-free subsets of [1,n]. Since the ... ρ). The main result of this note says that if (k − )/ is small in terms of ρ, then the number of (k, )-sum-free subsets of [1,n]isequalto(ϕ(ρ)+ϕ r...

Ngày tải lên: 07/08/2014, 06:20

... with b fixed, for < /b> various ranges of < /b> k. For < /b> purposes of < /b> comparison, we repeat these results below. Theorem 1 The < /b> distribution of < /b> the < /b> height of < /b> b- tries < /b> has the < /b> following asymptotic < /b> expan- sions for < /b> ... u − 1=O (b −1/2 ). We thus set u =1+x/ √ b and obtain I = e b b b+ 1 b!  B − √ b exp  b  lo...

Ngày tải lên: 07/08/2014, 06:20

... edge connected then the expected length of a minimum spanning tree is ∼ n r ζ(3). If we omit the edge connectivity condition, then it is at most ∼ n r (ζ(3) + 1). 1 Introduction Given a connected ... first give a rather precise description of mst(G). Lemma 1 [1] For any connected graph G, mst(G)=  1 p=0 E(κ(G p ))dp − 1. (3) A note on random minimum length spanning trees Al...

Ngày tải lên: 07/08/2014, 06:20

... inversions. Preprint, May 1996. A note on major sequences and external activity in trees Janet S. Beissinger Institute for Mathematics and Science Education The University of Illinois at Chicago (M/C 250) 950 ... S. Beissinger. On external activity and inversions in trees. J. Combin. Theoy Ser. B, 33(1):8792, 1982. [2] A. Bjăorner. The homology and shellability...

Ngày tải lên: 07/08/2014, 06:22

... K k -cross free if it does not contain k sets A 1 , , A k such that A i cross A j for every i = j. Karzanov and Lomonosov conjectured that for any fixed k, the maximum size of a K k -cross free ... [4]). However one can obtain asymptotically similar results for strongly-crossing by the next Theorem. Let G be a graph on k vertices v 1 , , v k . Then F is a G-strongly-cross free...

Ngày tải lên: 07/08/2014, 15:22

... ∆ = 3 (3-connected): ∆  4 (∆- edge-connected): K ⌊ ∆ 2 ⌋ K ⌈ ∆ 2 ⌉ K ⌈ ∆ 2 ⌉ K ⌊ ∆ 2 ⌋ ⌊ ∆ 2 ⌋ ⌈ ∆ 2 ⌉ ⌈ ∆ 2 ⌉ ⌊ ∆ 2 ⌋ Figure 2: K − ∆+ 1 -free graphs of high edge-connectivity with no precolouring ... to any proper ∆- colouring. ∆  3, |P | = 2: ∆  3, |P | = ∆: K − ∆+ 1 K − ∆+ 1 K − ∆+ 1 K − ∆+ 1 K − ∆+ 1 K ∆...

Ngày tải lên: 07/08/2014, 21:21