Báo cáo toán học: "total weight choosability of graphs" pptx

... of L are linear combinations of columns of A and neither of the columns of A appears more than once in these linear combinations. Therefore, by lemma 6, tmind(G) = 1. the electronic journal of ... a collection of lists of size 2 assigned to the vertices and the edges of a complete graph G = K n . There are (at least) two neighbour distinguishing total weightings of G with...

Ngày tải lên: 08/08/2014, 14:23

... for total 4 -choosability, and it completes the proof of Lemma 8. ✷ Lemma 9. If a nontrivial sepachain G 1 is good for total 4 -choosability, then so is the sepachain G in Fig. 1(h). Proof. Let Λ ... Λ-colouring of G, and this completes the proof of Lemma 5. ✷ Lemma 6. If a nontrivial sepachain G 1 is good for total 4 -choosability, then the sepachain G in Fig. 1(f) is very good for tot...

Ngày tải lên: 07/08/2014, 13:21

... independence number of general graphs of a given odd girth. We shall prove some similar bounds to those we prove for regular graphs in terms of a measure of the concentration of edges. Monien and ... for the independence number in terms of the odd girth, but instead of the average degree of the graph we have to use another measure of the concentration of edges. 8 Reference...

Ngày tải lên: 07/08/2014, 06:20

... B ⊆ A of measure µ(B) ≥ µ(A) 2 . (SL) Every measurable set A ⊂ Ωofmeasure0<µ(A) < 1 contains a symmetric subset B ⊆ A of measure µ(B) >µ(A) 2 . (U) ms(Ω,r) ≤ 1/r 2 . The proof of (L) ... colors of {a, b, c} and colors of {−a, −b, −c} do not intersect and, hence, {h(a),h(b),h(c)} and {h(−a),h(−b),h(−c)} are disjoint sets of vertices of the triangle T . Therefore, convex...

Ngày tải lên: 07/08/2014, 06:22

... [γ(K m )+1,g A −1], none of the genera admits the genus embedding of any the electronic journal of combinatorics 9 (2002), #R38 25 construction of graph H IB (s, k, l) up through the selection of faces F 1 through ... l)) = 2l +3. Proof: The proof proceeds just as in the proof of Theorem 3.2. For Part (i), the only difference is that here for H IB (s, k, l) we have deleted one edge...

Ngày tải lên: 07/08/2014, 07:21

... Severini Department of Mathematics and Department of Computer Science University of York, York YO10 5DD, U.K. ss54@york.ac.uk Richard C. Wilson Department of Computer Science University of York, York ... for some p, is presumably different from the support of M( −→ LD G ) p . This is because of the contribution of the negative entries in U(G). On the basis of this observation...

Ngày tải lên: 07/08/2014, 13:21

... possible, each of the selected (k + 1)-subsets will contain k+1 2 elements of C 1 and k+1 2 elements of C 2 . If k + 1 is odd, each of the selected (k + 1)-subsets will contain k 2 + 1 elements of C 1 and k 2 elements ... contain k 2 + 1 elements of C 1 and k 2 elements of C 2 . Assign each of these (k + 1)-subsets of colours to one vertex of the set X and to one vertex o...

Ngày tải lên: 07/08/2014, 15:22

... no vertex of T 0 is adjacent to any vertex of L. The distance of any vertex in T 0 from the farthest vertex in C is at most r + i/2. The distance of any vertex in the previous copies of T r p in ... journal of combinatorics 18 (2011), #P108 3 of degree one and let v be any such vertex of G. Set G ′ = G \ v. We may assume that H contains an induced copy of G ′ . Denote this c...

Ngày tải lên: 08/08/2014, 14:23

... coloring of G, so D ℓ (G) = 2. Lemmas 2–5 provide the necessary machinery to complete the proof of Theorem 2, and we do so now. Proof. (of Theorem 2) When n > 10 there must be an orbit of order ... 05C25 Abstract A coloring of the vertices of a graph G is said to be distinguishing provided that no nontrivial automorphism of G preserves all of the vertex colors. The dis- ting...

Ngày tải lên: 08/08/2014, 14:23

... ‘safely’ be seen as a ‘random subset’ of F q or, equally, as the output of an experiment of ran- dom and independent selection of elements of F q , the probability of picking up a particular one being ... first column of a normalized Hadamard matrix of order 4t, the set of all the rows of the remaining matrix can be seen (by replacing each occurrence of a −1 with 0) as a...

Ngày tải lên: 07/08/2014, 06:20