Báo cáo toán học: " Neighbour-distinguishing edge colourings of random regular graphs" ppt

... adjacent to edges coloured α, β and so is w, and all adjacent vertices of H 2 the electronic journal of combinatorics 13 (2006), #R77 7 Neighbour-distinguishing edge colourings of random regular ... proper edge colouring of a graph is neighbour-distinguishing if for all pairs of adjacent vertices v, w the set of colours appearing on the edges incident with v is not e...

Ngày tải lên: 07/08/2014, 13:21

... most two) edges of G − v − uw incident with wz  , and we proceed similarly if the color of the edge uz is γ. This way we obtain the desired L -edge- coloring λ of G − v − uw. Such an L -edge- coloring ... this L -edge- coloring can be extended to an L -edge- coloring of G, because every edge of C is incident with at most k − 2edgesofG  . If (d) of Lemma 2.1 holds, then let G...

Ngày tải lên: 07/08/2014, 06:20

... then each of G 1 and G 2 can be a single edge, a path of two edges, or nontrivial, except that G 1 and G 2 cannot both be single edges since G is simple. If G 2 , say, is a single edge, then ... graph T (G) of G. In the context of this paper, by a 4-list-assignment Λ to a graph G we always mean an assignment of a list Λ(z) of four colours to every element (vertex or edge) z of...

Ngày tải lên: 07/08/2014, 13:21

... weights, the degree of a vertex is shown to depend on the weight of that particular vertex and on the distribution of the weights of the other vertex type. 1 Introd uction Random intersection ... variant of the standard random intersection graph model in which random weights are assigned to both vertex types in the bipartite structure. Under certain assumptions on the d istrib...

Ngày tải lên: 08/08/2014, 11:20

... can ‘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 ... a Hadamard matrix of order 4t exists. Thinking probabilistically, one could see a codeword in C(q,n) as a random subset’ of F q or, equally, as the output of an experiment of...

Ngày tải lên: 07/08/2014, 06:20

... isomorphism of Proposition 5.1 we transfer our probability distribution to the set of m–tuples of Young disgrams with total number of boxes equal to n. Then by (5.2) we see that the probability of an ... length of the longest increasing subsequence for signed permutations em- bedded into the symmetric group of odd order can also be interpreted in terms of rim hook tableaux, se...

Ngày tải lên: 07/08/2014, 06:20

... graphs of f and g.Every bijection between two n-element subsets of N is similar to a unique permutation of [n]. For two permutations σ and π, σ contains π iff a subset of σ (regarded as a set of pairs) is ... system of 2 ℵ 0 subsets of A such that the set difference of every two distinct members of the system is infinite. For the notational convenience we identify A with N. the...

Ngày tải lên: 07/08/2014, 07:21

... copies of matrices. This leads to two types of evaluation formulas for the permanent of copies of matrices A . One in terms of certain orientations of A , the other in terms of colorings of A . ... proper coloring c: V (G)  v −→ c v ∈ C v of G exists. 2.3 Edge colorings of n -regular graphs The edge colorings of a graph are the vertex colorings of its line graph...

Ngày tải lên: 07/08/2014, 13:21

... several properties of a maximal IC-coloring f of K m,n . Proposition 3.3. If f is a maximal IC-coloring of G = (A, B) = K m,n , then all the colorings of vertices of G are distinct. Proof. Suppose, ... have the electronic journal of combinatorics 15 (2008), #R43 9 By Proposition 3.1, it contradicts to the assumption that f is a maximal IC-coloring of G and we have the proof of...

Ngày tải lên: 07/08/2014, 15:23

... (5) The proof of (3) is completely combinatorial, the proof of (4) uses nothing more than the fundamental theorem of algebra, and the proof of (5) is a simple geometric argument. Proof of (3). The ... result expressing the number of stan- dard tableaux of shape λ in terms of the lengths of the hooks in the diagram of λ. Many proofs of this fact have been given, of vary...

Ngày tải lên: 07/08/2014, 15:23