Báo cáo toán học: " Constructing fifteen infinite classes of nonregular bipartite integral graphs" doc

... electronic journal of combinatorics 15 (2008), #R8 23 Constructing fifteen infinite classes of nonregular bipartite integral graphs ∗ Ligong Wang 1,† and Cornelis Hoede 2 1 Department of Applied Mathematics, ... new method of constructing fifteen infinite classes of integral graphs is presented. In getting the results we proceed as follows: firstly, we give th...

Ngày tải lên: 07/08/2014, 15:22

... electronic journal of combinatorics 12 (2005), #R65 6 Both Q k and the grid Z n are cartesian products of paths either of length 2 (P 2 )or of infinite length (P ∞ ). We study the existence of perfect ... common generalization of 1-error binary perfect codes and perfect single error correcting codes in Lee metric, namely perfect codes on products of paths of length 2 and of...

Ngày tải lên: 07/08/2014, 13:21

... The set of climbing elements in W coincides with the set of Coxeter- sortable elements of W. Proof: By Theorem 1.1 of [9] the Coxeter-sortable elements of W are precisely the minima of the equivalence ... the minima of the equivalence classes of (W, ∼). By Theorem 4.2 and the proof of C orollary 3.6, the climbing elements are also the minima of these equivalence classes...

Ngày tải lên: 08/08/2014, 12:23

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Ngày tải lên: 05/08/2014, 09:46

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Ngày tải lên: 05/08/2014, 15:20

... proof of Lemma 1. 4 The General Plan For simplicity in this overview we ignore questions of uniformity. Given a set K,letK denote the sum of the elements in K.LetE(r, k, n)bethe number of k-subsets ... number of cycles violate (b) because the parity of the number of cycles in the structure D chosen there must be opposite the parity of |S| so that the final structure will have...

Ngày tải lên: 07/08/2014, 07:21

... number of par- titions of [n] containing exactly k blocks where k is fixed according to the number of o ccur rences of a subword pattern τ for several classes of patterns, includ ing all words of ... Stirling number of the second kind. We now provide a combinatorial proof of Corollary 2.12. By Lemma 2.5, to complete the proof, we must show that the total number of non-prima...

Ngày tải lên: 08/08/2014, 11:20

... v) is called an ancestor of u. By Theorem 6.6 of [2], in every DFS tree if w and w ′ are adjacent, then one of them is a ncestor of another. In a graph G, a k-coloring of G is a function c : V ... because of the minimality of the order of C, there is no edge between two vertices of the same color and for each i, 0 ≤ i ≤ k − 1, there is a v i -colorful pa th on C. As a conseq...

Ngày tải lên: 08/08/2014, 12:23

... and death of mature oak trees [17, 18]. Stimulated by that work, we began a survey of Phytophthora in deciduous forests of NE France. This work is in support of a larger ... a genus of plant pathogens, and indeed pathogenicity to oak has been demonstrated [17] for most of the species identified here. The wide- spread occurrence of th...

Ngày tải lên: 08/08/2014, 14:21

... section of each type and the attachment and relaying will be terminal. If on the other hand the axis is indeterminate there will often be several sections of each type and the attachment of sub- sequent ... option of con- centrating on different aspects and so discovering differ- ent regularities in the total pattern of the architecture of trees. 4.4 Implications The greatest impo...

Ngày tải lên: 08/08/2014, 14:22