Báo cáo toán học: "Minimum Weight H-Decompositions of Graphs: The Bipartite Cas" doc

... −1                  , where the first n columns correspond with the subsequent edges of the outer cycle, the next n, with the spokes of the wheel, and the remaining n + 1 ones are associated with the vertices (where the ... 0. Note that the columns of L are linear combinations of columns of A and neither of the columns of A appears more than...

Ngày tải lên: 08/08/2014, 14:23

... assign a weight of b to each H-subgraph in the decomposition and a weight of 1 to single edges. The total weig ht of the deco mposition is the sum of the weights of all elements in the decomposition. ... is either a single edge or forms an H-subgraph. We assign a weight of b to each H-subgraph in the decompo- sition and a weight of 1 to single edges. The...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:21

... pairs of the previous section; the witness bootstrapping process here gives the same witnesses constructed in the proof of the theorem. This also gives a simplified proof of the 2 × b case: by the ... shifted diagrams. The role of the rectangle is played by the staircase partitions S = n 321,andthe complement of λ ⊆ S is the remaining boxes of S reflected thr...

Ngày tải lên: 07/08/2014, 07:21

... M(G) j,m . Proof. Let G be a srg(n, k, r, s). Let A = M(G)andU = U(G). We define the amplitude of a given path to be the product of the entries of U corresponding to the transitions along the path. The ... this work. We would like to thank the anonymous referees for their help in improving the content and the presentation of the paper. One of the referees noted...

Ngày tải lên: 07/08/2014, 13:21

... L) in the B-game. the electronic journal of combinatorics 14 (2007), #R26 9 colours of C 1 and  k+1 2  colours of C 2 appear in X. If he can do so, then in the remaining part of the game the ... 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 of...

Ngày tải lên: 07/08/2014, 15:22

... to bipartite graphs. We shall make use of this result in proving the following theorems. Similar to the concept of (δ, χ)-bounded families is the concept of χ-bounded families. A family F of ... f orm). In the following theorem for any set C of graphs, F orb(C) denotes the class of graphs that contains no member of C as an induced subgraph. Theorem 1. ([10]) For any...

Ngày tải lên: 08/08/2014, 14:23

... h ∈ Γ} be the stabilizer and orbit of v under the action of Γ o n G. The order of the orbit of v under the action of Γ on G is |Aut(G)|/|St(v)|. Also, we let N G (x) denote the set of vertices adjacent ... then D ℓ (G) = 2. Proof. The proof of this lemma is identical to the proof of the correspo nding lemma in [AC96]. Let u 1 , . . . , u t be vertices from ea...

Ngày tải lên: 08/08/2014, 14:23

... t>0. The proof is straightforward. It should be noted that the values t = k(1 − k)/2 used in the proof of Theorem 5.1 lie outside the region t>0. Quite similarly to the case of the Young ... as follows: the vertices of the nth floor S n are the strict partitions of n, and the edges are the couples µ  λ. By definition, the empty partition ∅ is included into...

Ngày tải lên: 07/08/2014, 06:20