Báo cáo toán học: "he circular chromatic index of flower snarks" pps

... the circular chromatic index of F 3 : Theorem 2. The circular chromatic index of F 3 is 7/2. Proof. A 7/2 -circular edge-coloring of F 3 can be found in Figure 2. By Theorem 1, the cir- cular chromatic ... edges e and f of G. The circular chromatic index of G is the infimum (in fact, the minimum) of all r > 0 such that G has an r -circular edge-coloring. Th...

Ngày tải lên: 07/08/2014, 13:21

... one of the graphs of type A in Fig. 1, and this completes the proof. ✷ Lemma 10 Let G be an incompatible graph and suppose λ ∗ (G) = 3. Then G is isomorphic to a graph of type B of Fig. 1. Proof. ... definition, no pair of distinct edges of S belong to the same matching of size 3 of G. Since, in o rder to cover G we need to cover the edges of S, at least s(G) = |S| matchings...

Ngày tải lên: 08/08/2014, 01:20

... 2. y u <y v . Repeating the proof of Case 1 with roles of A and B switched yields this case. The proof of Claim 3.2 is the same (with C in place of B). ProofofClaim3.3.Let A ∗ =2A, B ∗ = A ∗ − ... Theorem 2. ProofofTheorem2. Let A be a member of a set M = {M i } of translates of a centrally symmetric convex set in the plane such that the clique number of the intersection gr...

Ngày tải lên: 07/08/2014, 08:20

... coloring of a k-graph is a coloring of its vertices such that no edge is monochromatic, and the chromatic number is the minimum number of colors in a proper coloring. An easy consequence of the ... tending to 1, the maximum degree ∆ of G satisfies ∆ < n k−1−1/ρ . Let us now delete the edges of a maximal collection of edge disjoint copies of members of F from G p . The re...

Ngày tải lên: 07/08/2014, 21:20

... definition of f(π) given in the paper of Dohmen et al [DPT03]. By abuse of notation, we write e ⊆ π to mean the vertex set of e is a subset of some block of π. Finally, let k 1 (π) denote the number of ... theorem that expresses the multivariate chromatic polynomial of H in terms of coboundary polynomials of section hypergraphs of H. This generalizes a result of Dohme...

Ngày tải lên: 08/08/2014, 14:23

... cd -index of [u, v], and it is denoted by  ψ u,v (c, d). Notice that the complete cd -index of [u, v] is an encoding of the distribution of the descent sets of each path ∆ in the Bruhat graph of ... terms of degree k − 1 (corresponding to paths of length k), then it also has terms of degree k + 1 (corresponding to paths of length k + 2). There are some specializations...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 09:46

... 2, . the electronic journal of combinatorics 11 (2004), #R22 2 2 Very-well-poised preliminaries The right-hand side of (1) defines the so-called Legendre transform of the sequence {c (r) k } k=0,1, ... l + j n − l − j  r , the electronic journal of combinatorics 11 (2004), #R22 3 On a combinatorial problem of Asmus Schmidt W. Zudilin ∗ Department of Mechanics and Mathematics Mosco...

Ngày tải lên: 07/08/2014, 08:20

... fol- lows. The oriented chromatic index χ  o (G) of an undirected graph G is the maximum of the oriented chromatic indexes taken over all the orientations of G (an orientation of an undirected graph ... of vertices of G to the set of vertices of H such that −−−−−−→ ϕ(u)ϕ(v)isan arc in H whenever −→ uv is an arc in G. The oriented chromatic index of an oriented gra...

Ngày tải lên: 07/08/2014, 13:21

... vertices of G of the weights of the spins times the product over the edges of G of the weights of the spin-pairs. In this language Z W (G) is the partition function of the the electronic journal of ... tight in the case of a family of graphs satisfying βd = ω(1). We give the proof ofTheorem 1.3in Section 3. An important tool in theproof is an extension of Theorem 1.1 to...

Ngày tải lên: 07/08/2014, 13:21