Báo cáo toán học: "On-line Ramsey Theory for Bounded Degree Graphs" doc

... Jiang, K.G. Milans, and D.B. West, Degree Ramsey number of cycles is bounded, submitted. [16] H.A. Kierstead and G. Konjevod, Coloring number and on-line Ramsey theory for graphs and hypergraphs Combin ... on-line degree Ramsey numbers for trees and cycles, draft. [18] W.B. Kinnersley, K.G. Milans, and D.B. West, Degree Ramsey numbers of graphs, submitted. [19] J. Neˇset...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 15:20

... of anti -Ramsey numbers for Ω k Unlike graphs in the family Ω 2 , we have no more information about graphs in the family Ω k for k ≥ 3. So we cannot treat the family Ω k (k ≥ 3) as we did for the ... anti -Ramsey numbers o f cycles, J. Graph Theory 47 (2004), 9-28. [4] B. Bollob´as, Extremal Graph Theory, Academic Press, New York, 1978. [5] P. Erd˝os, M. Simonovits, and V.T. S´os,...

Ngày tải lên: 08/08/2014, 01:20

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

... binomials of the form x α i −  j=i x β j j .Nowuse induction on the degree of such binomials. Let J = p 1 ,p 2 ,p 3 .IfJ = I, then choose b = x α i −  j=i x β j j of smallest degree in I\J. By ... s 12 and s 13 are nonzero: then either b  = x i b  for some binomial b  and i = 2 or 3. The degree of b  is less than that of b,sob  ∈ J; therefore b  would be too. Conseque...

Ngày tải lên: 07/08/2014, 08:20

... L n . Therefore by induction π = π 0 π n−2 π n−1 with π j ∈ R L j for all 0 ≤ j ≤ n − 1. For example, let π =[3, 5, −4, 2, −1], then π 3 = a 3 a 2 a 1 ; ππ −1 3 =[−4, 3, 2, −1, 5], there- fore π 2 = ... 3.1 and 3.3]. For a proof of the general case, see for example [2, Ch. 3.3]. the electronic journal of combinatorics 11 (2004), #R83 3 From this formulation one sees immediately that...

Ngày tải lên: 07/08/2014, 08:22

... vertex. However, in constructing W (n, 2k +2) we have forbidden this to occur for spokes this close. Thus no cycle of length l exists. Lemma 2 For any edge e in the complement of W (n, 2k +2) and ... value of this function for a given graph F has been quite difficult, and is known for relatively few graphs. K´aszonyi and Tuza in [12] proved the best known general upper bound for sat(n...

Ngày tải lên: 07/08/2014, 13:21

... property “minimum degree at least k” is increasing, the result for larger ω follows by a simple coupling argument applied to G (n, m, ·). The vertex degree analysis becomes complex for α near 1 due ... the degree distribution [18] and the phase transition [13] for α = 1. Although they consider p near phase transition threshold, they show that, for some properties, there is a val...

Ngày tải lên: 08/08/2014, 12:23

... Int. J. Number Theory, 6 (2010), 673–680. [6] H C. Chan, Ramanujan’s cubic continued fraction and Ramanujan type congruences for a ceratin par titio n function, Int. J. Number Theory, 6 (2010), ... was also proven by Baruah and Ojah [1] using the 3-dissections for ϕ(−q) −1 and ψ(q) −1 , and by Cao [4] applying the 3-dissection for (q; q) ∞ (q 2 ; q 2 ) ∞ . We will give another proof b...

Ngày tải lên: 08/08/2014, 14:22