Báo cáo toán học: "All Ramsey numbers r(K3, G) for connected graphs of order 9" pps
Báo cáo toán học: "Small Ramsey Numbers" doc
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Báo cáo toán học: "ON RAMSEY MINIMAL GRAPHS" doc
... C.C.Rousseau and R.H.Schelp, Ramsey minimal graphs for starforests, Discrete Math. 33 (1981), 227–237.[4] S.A.Burr, P.Erd˝os, R.J.Faudree, C.C.Rousseau and R.H.Schelp, Ramsey minimal graphs for match-ings,inThe ... Threshold functions for Ramsey properties,submitted.Key words and phrases: critical graphs, Ramsey theory1991 Mathematics Subject Classifications: 05D10, 05C804 ON RAMSEY MINIMAL GRAPHSTomasz ... R.J.Faudree, C.C.Rousseau and R.H.Schelp, Ramsey minimal graphs for forests,Discrete Math. 38 (1982), 23–32.[6] S.A.Burr, P.Erd˝os, R.J.Faudree and R.H.Schelp, A class of Ramsey- finite graphs,inProc.9thS.E.Conf....
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Báo cáo toán học: "Explicit Ramsey graphs and orthonormal labelings" pdf
... isΩ(m4/3).Here we improve this bound and describe an explicit construction of triangle free graphs withindependence numbers m and Ω(m3/2) vertices. Our graphs are Cayley graphs and their construc-tion ... Tough Ramsey graphs without short cycles, to appear.[3] N. Alon and N. Kahale, in preparation.[4] N. Alon and J. H. Spencer, The Probabilistic Method, Wiley, 1991.[5] F.R.K.Chung,R.CleveandP.Dagum,A ... Mathematics (AMS 1983), 67-70.[10] J. H. Kim, The Ramsey number R(3,t) has order of magnitude t2/ log t, to appear. Explicit Ramsey graphs and orthonormal labelingsNoga Alon∗Submitted: August...
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Báo cáo toán học: " DESCENDANTS IN HEAP ORDERED TREES OR A TRIUMPH OF COMPUTER ALGEBRA" ppsx
... number of descendants and ascendants in random search trees. In preparation, 1996. DESCENDANTS IN HEAP ORDERED TREES OR A TRIUMPH OF COMPUTER ALGEBRAHelmut ProdingerInstitut făur Algebra und ... and myself are currently investigating thisparameter (and several others) for binary search trees and some variants.For more information about heap ordered trees the reader is referred to [1], ... concentrate on the number of descendants of the node j in a (random) heap ordered tree of size n ≥ j. By convention, we say that the node j is a descendant of itself. For instance, node 1 always has...
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Báo cáo toán học: "All Ramsey numbers r(K3, G) for connected graphs of order 9" pps
... 1998AbstractWe determine the Ramsey numbers r(K3 ,G) for all 261080 connected graphs of order 9 and further Ramsey numbers of this type for some graphs of order up to 12. Almost all of them were determined ... containingtriangle-free graphs of order r which are (or might be) Ramsey graphs for (K3,H) the electronic journal of combinatorics 5 (1998), #R7 32 Computing r(K3,H) for graphs of order 9We computed the Ramsey ... and Ramsey theory meet.Here we will deal with Ramsey numbers r(K3,H) for connected graphs H of small order. A few years ago, these numbers were completely determined only for graphs H up to order...
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Báo cáo toán học: "On Kissing Numbers in Dimensions 32 to 128" pptx
... 07 932- 0971, USASubmitted: April 9, 1998; Accepted: April 13, 1998ABSTRACTAn elementary construction using binary codes gives new record kissing numbers in dimensions from 32 to 128.1. IntroductionLet ... 1,260,230,400 in dimensions 32, 64 and 128, for example). In contrast, Quebbemann’s lattice Q 32 [14], [5, Chap. 8] has τ = 261,120. In recent years the kissing numbers of a few other lattices in dimensions ... kissing numbers of the best lattices known. On Kissing Numbers in Dimensions 32 to 128Yves EdelMathematisches Institut der UniversităatIm Neuenheimer Feld 28869120 Heidelberg, GermanyE. M. Rains...
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Báo cáo toán học: "On the Stanley-Wilf conjecture for the number of permutations avoiding a given pattern" ppt
... a given patternRichard ArratiaDepartment of MathematicsUniversity of Southern CaliforniaLos Angeles, CA 90089-1113email: rarratia@math.usc.eduSubmitted: July 27, 1999; Accepted: August 25, ... 1999.Abstract. Consider, for a permutation σ ∈Sk,thenumberF(n, σ) of permuta-tions in Snwhich avoid σ as a subpattern. The conjecture of Stanley and Wilf isthat for every σ there is a constant ... 2. There exists an n-permutation, with n = k2, containing every k-permutationas a subpattern; i.e. m(k) ≤ k2. On the Stanley-Wilf conjecture for the number of permutations avoiding a given patternRichard...
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Báo cáo toán học: A Ramsey Treatment of Symmetry" pptx
... Janos Bolyai Mathematical Society, 30–32.[2] T. Banakh. On a cardinal group invariant related to partitions of Abelian groups(in Russian). Mat. Zametki, 64(3):341–350, 1998. English translation ... Russian). Izvestiya Ross. Akad. Nauk, Ser. Mat. (Russian Academy of Sciences. Izvestiya. Mathematics), 2000, to appear.[6] E. R. Berlekamp. A construction of partitions which avoid long arithmetic ... compact Abelian groupsRecall that we consider a compact Abelian group G along with its Haar measure à.The topology of G is assumed Hausdor, and à is assumed to be a complete probabilitymeasure....
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Báo cáo toán học: "All regular multigraphs of even order and high degree are 1-factorable" docx
... 1-factors of G. This gives a decomposition of the edges of G into 2r 1-factors of G,a(k + 1) -regular simple graph, and (r − 1) k -regular simple graphs.3 1-factorization of regular multigraphs of even ... ,r2 are Hamilton cycles of G, F1,F2, ,F(r−1) are 1-factors of G, F is a simple (k +1)-factor of G,andS1,S2, ,S(r−1) are k -regular simplesubgraphs of G.Sincen is even, each of the ... subgraphF of G such that degF(v)=f (v) for each v ∈ V (G). For X, Y ⊆ V (G)wedenotethe electronic journal of combinatorics 8 (2001), #R41 3 All regular multigraphs of even order and high degree are...
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Báo cáo toán học: " Exchange Symmetries in Motzkin Path and Bargraph models of Copolymer Adsorption" ppsx
... factorisation of Motzkin paths.2.1 Motzkin Paths with Vertex-visits Motzkin paths may be factored recursively in terms of shorter Motzkin paths. In particu-lar, every adsorbing Motzkin path is either ... model of an adsorbing polymer can be defined by letting the path be attractedto an adsorbing line. In models of Motzkin paths, the adsorbing line will be the maindiagonal of the lattice, and it ... would be Motzkin paths [9], which is amodel of (fully) directed paths on a triangular lattice, and confined to step only abovethe main diagonal. In both models of bargraphs and Motzkin paths,...
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Báo cáo toán học: "Outerplanar Crossing Numbers, the Circular Arrangement Problem and Isoperimetric Functions" doc
... his thesis the circular arrangement problem for the hypercube, and Bezrukov and Schroeder [1], who showed that for trees the solutionsfor the linear arrangement problem and the circular arrangement ... bound for the usuallinear arrangement problem. Recall that the linear arrangement problem requires the placement of the vertices of the graph into integer positions, and minimizes the sum of ... The upper bound follows from Theorem 1. The lower bound follows from Theo-rem 2 and the isoperimetric inequality in Theorem 8, (35).Remark 1. Note that Theorems 11, 12 fail for k = n, and therefore...
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Báo cáo toán học: "Explicit Ramsey graphs and Erd˝s distance problems o over finite Euclidean and non-Euclidean spaces" ppt
... Section 2 we construct our main toolsto study the Erd˝os problem over finite Euclidean and non -Euclidean spaces, the finite Eu-clidean and non -Euclidean graphs. Our construction follows one of Bannai, ... concise, we will restrict our discussion to the finite non- Euclidean graphs obtained from the action of the simple orthogonal group on the set ofnon-isotropic points. Similar results hold for ... action of simple orthogonal group O ±2m(q) (qodd) on the set of non-isotropic pointsLet V =2mqbe the 2m-dimensional vector space over the finite fieldq(q is an odd primepower). For each...
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Báo cáo toán học: "The Ramsey number of diamond-matchings and loose cycles in hypergraphs" potx
... pl} and we join vertices x and the electronic journal of combinatorics 15 (2008), #R126 10 The Ramsey number of diamond-matchings and loose cycles in hypergraphsAndr´as Gy´arf´as∗Computer and ... [12]) and t = 2 (Alon and Frankl [1] and Gy´arf´as[13]).Next we state and prove the Ramsey- type form of our main result, it determines theexact value of the Ramsey number of a diamond-matching.the ... subhypergraph of H.The key in our proof of Theorem 1 is a compression lemma. We use T and N in itsformulation instead of H and n to avoid misunderstanding when we apply it to subhyper-graphs of H....
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Báo cáo toán hoc:" Anti-Ramsey numbers for graphs with independent cycles Zemin Jin" ppt
... 8 Anti-Ramsey numbers for graphs with independent cycles Zemin JinDepartment of Mathematics, Zhejiang Normal UniversityJinhua 321004, P.R. Chinazeminjin@hotmail.comXueliang LiCenter for ... of anti-Ramsey numbers for ΩkUnlike graphs in the family Ω2, we have no more information about graphs in the familyΩk for k ≥ 3. So we cannot treat the family Ωk(k ≥ 3) as we did for ... 657-665.[6] T. Jiang, Edge-colorings with no la rge polychromatic stars, Graphs Combin. 18(2002), 303-308.[7] T. Jiang, Anti-Ramsey numbers of subdivided graphs, J. Combin. Theory, Ser.B, 85(2002),...
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Báo cáo toán học: " Cyclic Sieving Phenomenon in Non-Crossing Connected Graphs" pps
... 10.1].6.1 Cyclic sieving phenomenon in other types of graphs In [3], one finds various formulas f or counting classes of non-crossing graphs, of which (1)is one. Consider the following four generating ... let C be the cyclic g roup of order n acting on X by rotation. Then (X, X(q), C)exhibits the cyclic sieving phenomen o n.6.2 Unifying algebraic proof of cyclic sieving phenomenon in graphsSo ... would be interesting to see an algebraic proof of Theorem 1.1along the lines of [4, Proposition 2.1].the electronic journal of combinatorics 18 (2011), #P9 13 Cyclic Sieving Phenomenon in Non-Crossing Connected...
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