Báo cáo toán học: "Nowhere-zero 3-flows in squares of graphs" pdf

... 3-flow. In this paper, we give a complete characterization of graphs whose squares admit nowhere-zero 3-flows and thus confirm Tutte’s 3-flow conjecture for the family of squares of graphs. 1 Introduction All ... is contained in a circuit of length 3 or 4. By contradiction. Let G 1 be the graph obtained from G by deleting the edge e and adding a new vertex y  and a new edge xy...

Ngày tải lên: 07/08/2014, 07:21

... heterochromatic path of length l + 1, a contradiction to the choice of P . So, we get that i 1 /∈ C({u 1 v s ,u 2 v s , ,u l v s }). Now we turn to proving our main theorem. 4. Proof of Theorem 3.1 Proof. We ... vertex v in G with 8 ≤ k  ≤ k − 1. In the following, all the notations are the same as in Section 3. Since d c (v) ≥ k>k− 1 for every vertex v of G, G has a heteroch...

Ngày tải lên: 07/08/2014, 13:21

... the beginning of w. 4 Words containing in nitely many overlaps In this section we construct various in nite α power-free binary words containing in nitely many overlaps. We begin by considering ... Thus, each 1 in b introduces an overlap in w b . Since uncountably many binary sequences contain in nitely many 1’s, uncountably many of the w b are 7/3 power-free words containing i...

Ngày tải lên: 07/08/2014, 13:21

... (D i ) i∈I of subsets of E thin if no edge lies in D i for in nitely many indices i. Let the (thin) sum  F of this family be the set of all edges that lie in D i for an odd number of indices i, ... closed, every point in P \ C is contained in a C-arc in P. Suppose no C-arc in P is a shortcut of C. We can find a family (W i ) i∈N of countably many internally disjoint...

Ngày tải lên: 08/08/2014, 01:20

... duality between proper colorings and nowhere-zero flows, the second one uses an interpretation of a nowhere-zero point of a certain incidence matrix as a “nowhere-zero coloring” of the underlying graph. Part ... Orientations of Graphs. Combinatorica 12 (1992), 125–134. [AlTa2] N. Alon, M. Tarsi: A Nowhere-zero Point in Linear Mappings. Combin atorica 9 (1989), 393–395. the electronic...

Ngày tải lên: 08/08/2014, 14:22

... contracting u and v into one point. Let P ′ denote t his new lattice pat h and w the new point obtained by contracting u and v. Clearly, P ′ ∈ L N,S M and w is one of the minimum points of P ′ , ... The combination of P ′ and w yields a new interpretation of CF M (x, y) by defining (L N,S M , W) = {(P ′ , w) | P ′ ∈ L N,S M and w is one of the minimum points of P ′ }. The bivariate...

Ngày tải lên: 08/08/2014, 14:23

... k,ofG whoseedgesetscovertheedgesetofG. That is, each edge of G is in at least one of the bicliques in B.Thebiclique cover number, bc(G), of a graph G is the minimum number of bicliques in a biclique cover of G.Abiclique ... edges e of G. Proof. It follows immediately from (2) and (4) that bc ∗ (G) ≤ bp ∗ (G) since a weighting v of the edges of G that satisfies the constra...

Ngày tải lên: 07/08/2014, 13:21

... {u, v} and shrink the edge e to the edge e  by identifying u, v. e  remains chromatically active in C.k. the electronic journal of combinatorics 16 (2009), #R94 7 A λ-coloring of H is a function ... who studied a class of non-linear uniform hypergraphs which are named sunflower hypergraphs by Tomescu in [17]. In [18] Tomescu gave the following formula of the corresponding chrom...

Ngày tải lên: 08/08/2014, 01:20

... connected graphs in the whole pap er. Moreover, the cardinality of a set S will be denoted by #S. The notion of set coloring of a graph was introduced in 2 009 by Hegde [4]. In its original version, ... contradiction. • A cell of type 1 is in the same row as a cell of type 4. Denote by i the row index of these two cells of type 1 and 4. Then i + 2 n−1 is the index of a...

Ngày tải lên: 08/08/2014, 12:23

... (1) Theorem 4 is proved in Janson [4] (Theorem 11) and in Molloy, Robalewska-Szalat, Robin- son and Wormald [8]. 2 Proof of Theorem 1 We begin by letting Y be a set of size 2 rm consisting of r = O(1) copies ... satisfying the conditions of Theorem 3. There is a minor technical point in that we can only use Theorem 2 to prove the existence of a randomly coloured (multi-)graph...

Ngày tải lên: 08/08/2014, 11:20