Báo cáo toán học: "Competitive Colorings of Oriented Graphs" docx

... 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

... 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: ... σ. Proof. (Necessity) See the proof of Theorem 3.3 in [1]. (Sufficiency) Suppose Sp S (G σ ) = iSp(G) for any orientation σ. By Theorem 2.2, G is a bipartite graph. And s...

Ngày tải lên: 07/08/2014, 21:21

... spectrum of D a,b,0 (with δ  3). Lemma 3.4. The spectrum of D a,b,0 with δ = gcd(a, b)  3 consists of the eigenvalues of C δ (except 2 and −2) with multiplicity 3, the eigenvalues of C a and ... eigenvalues of C a ∪ C b and be of multiplicity 1. This ends the proof. From the above lemma we know to some extent the spectrum of D a,b,0 . If H is a tentative cospectral mate of...

Ngày tải lên: 08/08/2014, 12:22

... Oχ(K 5,5 )=5andOχ(K 5,4 )=5. ProofofTheorem1.4: Consider a d-degenerate ordering {v 1 , ,v n } of the vertices of G. We need to create a set {c 1 , ,c k } of k-orthogonal colorings. We prove the theorem by ... spanning subgraph of G r,r has a strong orthogonal scheme. Proof: We begin with the proof of the first part. It suffices to show that G r,r−1 has a SPOC. We define two colorings...

Ngày tải lên: 07/08/2014, 06:20

Ngày tải lên: 05/08/2014, 09:46

... 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

... result of Kannan, Tetali and Vempala to com- pletely solve, via a simple proof, the problem of random generation of a labeled tournament with a given score vector. The proof uses the method of path ... score vector of a tournament is the sequence of out- degrees of the vertices of the tournament. In general, given a score vector with n scores, there can be an exponential (in n...

Ngày tải lên: 07/08/2014, 06:20

... 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 ...  The chromatic polynomial χ G (x) of a graph G is a polynomial which evaluates to the number of proper colorings of G with x colors. The subgraph expansion of χ G (x)is χ G (x)=...

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

... 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