Báo cáo toán học: "Total 4-choosability of series-parallel graphs" pptx

Ngày tải lên: 05/08/2014, 15:21

... Subsquares of N 2 squares of order 9. In particular we note that there are 1589 main classes of N ∞ squares of order 9, yet only 37 of these contain pan-Hamiltonian squares. In terms of reduced ... have a generalisation of Lemma 4. §6. Small orders For n ∈{2, 3, 5} thecatalogueofLatinsquaresin[5]showsthatthereisasinglemain class of N ∞ square of order n,namelythatofC n . Acc...

Ngày tải lên: 07/08/2014, 06:20

... member of the second coordinate of the label of y, delete the edge x j y.If the digit of z is 3 and y is not a member of the second coordinate of the label of z, delete the electronic journal of ... Subclaims, the proof of our lemma is complete. 5 Proof of the Main Theorem In this section, we present the proof of the main theorem. Let C be a topologically closed class o...

Ngày tải lên: 07/08/2014, 06:23

... class of cographs. 3 Spectrum of a cograph The characteristic polynomial ϕ(X) of the graph X is the characteristic polynomial of its adjacency matrix A(X). The spectrum of X is the collection of ... of eigenvalues of A(X), or equivalently, the collection of zeros of ϕ(X). The rank of X is the number of non-zero values occurring in the spectrum. In order to study the sp...

Ngày tải lên: 07/08/2014, 07:21

... ordering of the vertices to an ordering of the edges lexicographically. A broken circuit of H ⊆ G is a set of edges B ⊆ H such that there is some edge e ∈ G, smaller than every edge of B, such ... consists of all edges of G with both ends in S. We will use the symbols π and σ to denote set partitions. The notation π  S means π is a set partition of the set S. The length (numb...

Ngày tải lên: 07/08/2014, 08:22

... one-factorization of type 4 + 4 + 4 is only possible for three graphs of order 12: the disjoint union of three copies of C 4 , the disjoint union of three copies of K 4 ,and the union of K 4 and the ... properties of the classified one-factorizations are also tabulated. 1 Introduction An r-factor of a graph G is an r-regular spanning subgraph of G.Anr-factorization of G i...

Ngày tải lên: 07/08/2014, 08:22

... yields the result that the absence of rainbow 5-cycles implies the absence of rainbow 9-cycles. Proof. The proof of this lemma has the same basic structure as that of Lemma 8, but the cycles we consider ... color of this chord. On the one hand, it must agree with one of the other edges of the n-cycle to avoid a rainbow n-cycle; on the other hand, it must similarly agree with one...

Ngày tải lên: 07/08/2014, 13:21

... δ) denote the set of neighbours and the degree of v in G, the set of vertices, the set of edges and the minimum degree of G, respectively. By G[D] we mean an induced subgraph of G with the vertex ... V 2 , . . . , V k } of disjoint subsets of a set V is called a partition of V if the union of all elements of V is V and V i = ∅ for every i. We shall denote as P k a path...

Ngày tải lên: 07/08/2014, 21:20

... University Press, 1987. the electronic journal of combinatorics 16 (2009), #N32 6 Skew Spectra of Oriented Graphs Bryan Shader Department of Mathematics University of Wyoming, Laramie, WY 82071-3036, USA email: ... underlying graph of G σ , and we denote by Sp(G) the adjacency spectrum of G. S kew-adjacency matrix S(G σ ) of G σ is intro duced, and its spectrum Sp S (G σ ) is ca...

Ngày tải lên: 07/08/2014, 21:21

... and at least one of them contains an end of an edge of A  i ∩ B  since at least one of G[X i ∩ Y ] and G[X i ∩ Y ] contains an end of an edge of A i ∩ B. the electronic journal of combinatorics ... G ∗ is necessarily connected. Each bond of G is a circuit of G ∗ , and each circuit of G is a bond of G ∗ . If a theorem holds for a given set T of edges of G, then the...

Ngày tải lên: 08/08/2014, 11:20