Báo cáo toán học: "New infinite families of almost-planar crossing-critical graphs" ppsx
Báo cáo toán học: "New infinite families of 3-designs from algebraic curves of higher genus over finite fields" potx
... construct new infinite families of 3-designs.1 IntroductionA t − (v, k, λ) design is a pair (X, B) where X is a v-element set of points and B is acollection of k-element subsets of X called blocks, ... Jangheon Oh and Hoseog Yu, New infinite families of 3-designsfrom algebraic curves over Fq, European J. Combin. 28 (2007), no. 4, 1262–1269.[10] K. Ranto, Infinite families of 3-designs from Z4-Goethals ... consequence, we obtain new infinite families of 3-designs. In particular, we get infinite family of 3-designs whose blocksize is congruent to 1 modulo p.2 Zero sets of algebraic curvesLet p be...
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Báo cáo toán học: "New infinite families of almost-planar crossing-critical graphs" ppsx
... communication and preprint of [2]) that typi-cal constructions of infinite families of simple 3-connected k -crossing-critical graphs createbounded numbers (wrt. k) of vertices of degrees other than ... in infinite families of k -crossing-critical graphs? We positively answerone half of his question in Theorem 3.1 and Proposition 2.1;• namely we construct, for all k > 2, infinite families of ... 332–341.[11] G. Salazar, Infinite families of crossing-critical graphs with given average degree,Discrete Math. 271 (2003), 343–350.[12] J.ˇSir´aˇn, Infinite families of crossing-critical graphs...
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Báo cáo toán học: "An infinite family of non-embeddable Hadamard designs" potx
... design in the infinite family has the collection of five blocks mentioned above then so do all other members of the infinite family;3) Give a design having the required collection of five blocks.Theorem ... matrix ofa2-(v, k, λ)designisab × v matrix A = aij,inwhich aij=1ifblocki contains point j and aij=0otherwise.3 ResultsThe strategy for establishing the existence of an infinite family of ... existence of an infinite family of non-embeddable 2 - (2λ +2,λ +1,λ)designs,λ =3(2m) − 1,m ≥ 1 is established.Mathematical Reviews Subject Number: 05B05Dedicated to the memory of George Mackenzie1...
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Báo cáo toán học: "An Infinite Antichain of Permutations" ppsx
... partially ordered set of finite permutations orderedby deletion of entries contains an infinite antichain. In other words, there exists an infinite collection of permutations no one of which contains ... than the poset of graphs ordered by the operations of edge contraction and vertex deletion. (That this poset of graphs does not contain an infinite antichain is a famous theorem of Robertson and ... Infinite Antichain of PermutationsDaniel A. SpielmanDepartment of MathematicsMassachusetts Institute of TechnologyCambridge, MA 02139spielman@math.mit.eduMikl´os B´onaDepartment of MathematicsUniversity...
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Báo cáo toán học: "Another infinite sequence of dense triangle-free graphs" docx
... structuralproperties and that the natural way to describe the structure of these graphsis in terms of graph homomorphisms. One infinite sequence of cores of densemaximal triangle-free graphs was known. All graphs ... 4-colourable, in contrast to a conjecture of Jin [8], saying that thereare graphs of arbitrarily large chromatic number with this property.Another infinite sequence of dense triangle-freegraphsStephan ... journal of combinatorics 5 (1998), #R43 4Figure 2: Υ16is composed of two parts. The graph on 8 vertices on the left to whichΓ8is attached on the right.triangle-free and the neighbourhood of...
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Báo cáo toán học: "An Infinite Family of Graphs with the Same Ihara Zeta Function" potx
... derivative of ZX(u)is a generating function for the number of circuits. See for instance [7]. Knowing thenumber of circuits of each length is sufficient to conclude the number of primitive circuits of ... demonstrate add itional families of pairs of graphs which share the same zetafunction.1. IntroductionIn 2009 , Cooper described an infinite family of non-isomorphic pairs of graphs which sheconjectured ... #R82 1•v1•v2Figure 3: ZProof. That X a nd Y have the same number of primitive circuits of length k for all kimplies equality of the zeta functions of X and Y follows directly from Definition...
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Báo cáo toán học: "Edge and total choosability of near-outerplanar graphs" ppsx
... 1, again contradicting the choice of G. This completes the proof of Claim 3.1. ✷In view of Claim 3.1 and Lemma 3.1, B must be K4-minor-free. By the proof of Claim 2.1, B ∼=K2, so that ... that every edge of G is given a list of ∆ colours.Then the edges of G − (B − z0) can be properly coloured from these lists. Since eachedge of B still has a residual list of at least 3 usable ... edge of G is given a list of ∆ + 1 colours. Thenthe vertices and edges of G − (B − z0) can be properly coloured from these lists. Eachedge of B incident with z0has a residual list of at...
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Báo cáo toán học: "Some gregarious cycle decompositions of complete equipartite graphs" ppsx
... decomposition of Kk+1∗ Kmwhenever k is odd and m is even .Proof As in the proof of L emma 3.12, we need only give a k-cycle decomposition of 2Kk+1which satisfies the conditions of Corollary ... vertices.In fact, since the sum-weight of each cycle in D is a multiple of λ, each of these subgraphsnecessarily consists of λ pairwise vertex-disjoint k-cycles, each of which is gregarious inG ∗ Kλ. ... further partitioning of each of the sets{v1, v2, . . . , vaℓ} into ℓ subsets, each of size a. It is these nℓ sets of size a which are con-sidered the partite sets of G ∗ Kℓ(a). Note...
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Báo cáo toán học: " Extremal infinite overlap-free binary words" potx
... prefix of x of length 5.Proof. Firstnotethatthewordyis necessarily overlap-free by assertion 1 of Lemma 2.The existence of the decomposition for finite words is proved in [10], in the proof of Theorem ... this factorization of x,thewordu(resp. v) depends only on the prefix (resp.suffix) of x of length 7. This is recalled in the following table of all possible prefixes (resp.suffixes) of length ≥ 7: by ... 10, and we extend it to infinite words by continuity. The infinite fixed point of µ beginning with 0 is denoted by t, hencet = 0110100110010110 ···.The infinite fixed point of µ beginning with 1 is...
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Báo cáo toán học: "Decomposing infinite 2-connected graphs into 3-connected component" pps
... atree.Proof: It suffices to prove that every edge of T (G) is an isthmus. Corollary 9 showsthat if [x, y] is any hinge of G, then the cleavage units of G are precisely the cleavage units of the ... of K,oneofH and J is 2-connected. It is straightforward to show thecorresponding one of Hand Jis also 2-connected, so that (H,J) is a hinge-separation of G. But then every edge of ... component L of G − V (H) by addingto L all the edges of G that have at least one end in L (together with all ends of theseedges).A hinge-separation of G is a 2-separation (H, K)ofG such that...
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