Báo cáo toán học: "A Note on Sparse Random Graphs and Cover Graphs" docx

... A Note on Sparse Random Graphs and Cover Graphs ∗ Tom Bohman † Alan Frieze ‡ Mikl´os Ruszink´o § Lubos Thoma ¶ 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 n...

Ngày tải lên: 07/08/2014, 06:20

... odd cycle. Recently, Albertson posed the following question. Take a graph described above, precolor a fixed set of vertices P in ∆ colors arbitrarily. Under what condition on P can we extend that ... ∈ E(G),p∈ P \{u 1 , ··· ,u t }. Note that if x ∈ V (G 2 ) is adjacent to more than one vertex of P 1 , these vertices must be u i and v i for some i, so only one of the above cases can hold....

Ngày tải lên: 07/08/2014, 07:21

... appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. A note on the almost sure limit theorem for self-normalized partial sums of random variables ... H ¨ ormann [8], Wu [9, 10], and Ye and Wu [11]. Huang and Zhang [12] and Zhang and Yang [13] obtained ASCLT results for self-normalized version. Under mild moment conditions A...

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... Theory of Graphs, Allyn and Bacon, Boston, 1971. Note on Maximal Nonhamiltonian Burkard–Hammer Graphs 399 exists a maximal nonhamiltonian Burkard–Hammer graph G = S(I ∪ K, E) with |I| = m and δ(G)=|I|−k ... =6+t, Note on Maximal Nonhamiltonian Burkard–Hammer Graphs 409 2. R. E. Burkard and P. L. Hammer, A note on hamiltonian split graphs, J. Combin. Theory Ser. B 28 (...

Ngày tải lên: 06/08/2014, 05:20

... m j , and hence that l is a subword of h ω (a). This contradicts Lemma 2.6. The supposition that m j encounters m i leads to a contradiction. We conclude that m i and m j are incomparable, and ... denoted by |w|. Thus |banana| = 6, for example. The language consisting of all words over Σ is denoted by Σ ∗ . If x, y ∈ Σ ∗ , the concatenation of x and y, written xy, is simply the string...

Ngày tải lên: 07/08/2014, 06:20

... representation of S n consists of the direct sum of the reflection representation and the trivial representa- tion. This trivial summand has no significant effect on the theory.) In this context it ... constant c>0 such that H(n) ≥ n 2 2 −cn 3/2 for all n ≥ 1. Proof. From the definition of H(n) and Proposition 3.2 (and the fact that the right-hand side of equation (5) is increasing), al...

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... (3) When conditioning on the event C P 0 , the random graphs of the resulting probability space may contain edges only from within the edges that connect vertices of different partitions of P 0 . ... Krizanc, and Y.C. Stamatiou, “Approximating the unsatisfiability threshold of random formulas,” Random Structures and Algorithms 12, pp 253–269, 1998. [11] V.F. Kolchin, Random Mapp...

Ngày tải lên: 07/08/2014, 06:20