Báo cáo toán học: "The spectral excess theorem for distance-regular graphs: a global (over)view" docx

...

Ngày tải lên: 05/08/2014, 10:20

... class="bi x0 y1 w2 h 2" alt =""

Ngày tải lên: 05/08/2014, 10:20

... alt =""

Ngày tải lên: 05/08/2014, 15:21

... alt =""

Ngày tải lên: 05/08/2014, 15:21

... of the classical finite and a ne Weyl groups, and certain families which generalize them. In all cases where W is a finite or a ne Weyl group, the denominators W (q) occurring in the left-hand ... q 2 ) −1 ∞ again by the q-binomial theorem. Furthermore, since the Coxeter diagram in the case has an edge labelled 4, there exists another additive statistic n(w), equal...

Ngày tải lên: 07/08/2014, 06:20

... 2-choosable? By Theorem 2.5, H(G) (from the above problem) is 2-colorable. This the- orem relies on the 4-Color Theorem. So, it would be an interesting problem to find a direct proof of Theorem ... proof of Lemma 2.3 (by possibly permuting the colors) so that the corresponding strong 3-coloring of H(G)is an extension of c. This completes the proof. Theorem 2.6 The...

Ngày tải lên: 07/08/2014, 06:20

... − 15 + 12 − 3=0 N char(dodecahedron) = 20 − 60 + 20 = −20 2 Computing the Neighborhood Characteristic The neighborhood characteristic of a graph can also be calculated in terms of the complete bipartite ... overcounting is corrected for in the following theorem (which also shows that, for a bipartite graph G, N char(G) equals twice the ‘bipartite characteristic defined in [5]). T...

Ngày tải lên: 07/08/2014, 07:21

... we give combinatorial proofs of the q-binomial theorem and Theorems 1.2 and 1.3. Our combinatorial proof of the q-binomial theorem is based on Theorem 2.1, and is essentially the same as that ... combinatorial proofs of these two identities and the q-binomial theorem by using conjugation of 2-modular diagrams. 1 Introduction We follow the notation and terminology in...

Ngày tải lên: 07/08/2014, 07:21

... The Tur´an problem for hypergraphs of fixed size Peter Keevash Department of Mathematics Caltech, Pasadena, CA 91125, USA. keevash@caltech.edu Submitted: ... a forest of given size. Lemma 2 (i) An r-uniform hypergraph with at least r!(t − 1) r edges contains a forest with t edges. (ii) Let F be a 3-uniform hypergraph. Then either (a) F contains a forest ... bounds are known...

Ngày tải lên: 07/08/2014, 08:22

... that admits no cover pebbling, all pebbles may be concentrated to one of the fat nodes 1 with cover pebbling still not possible. Proof. Start with a distribution that admits no cover pebbling. If ... cover pebbling from f exceeds the total value of the pebbles. Therefore, cover pebbling is not possible with all pebbles initially on f .  4 The cover number for some classe...

Ngày tải lên: 07/08/2014, 08:22

... contain at least one tip. The Edmonds-Gallai structure theorem can be formulated for the k-piece packing problem as follows. The classical Edmonds-Gallai theorem first defines the vertex set D to consist ... characterization for graphs having a perfect k-piece packing and a min-max result for the size of a maximum k-piece packing are derived. Neither the Edmon...

Ngày tải lên: 07/08/2014, 08:22

... this notation, we have e(x W → y) = y, W x . 3 The Induced Subgraph Order on Unlabelled Graphs Let V denote the set of isomorphism classes of simple graphs. Define a partial order on V by G ≤ ... The Induced Subgraph Order on Unlabelled Graphs Craig A. Sloss ∗ Department of Combinatorics and Optimization University of Waterloo, Ontario, Canada csloss@math.uwaterloo.ca...

Ngày tải lên: 07/08/2014, 13:21

... If p a contains more than one vertex (say p a = a, a 2 , a 3 , . . . , a n ), then (a, a 2 ) is lonely since p a is a path in L C (G). But {a} is a singleton color class, so (a 2 , a) is also lonely. ... 2007 Mathematics Subject Classification: 05C15 Abstract We prove that if G is a graph containing a doubly- critical edge and satisfying χ ≥ ∆ ≥ 6, then G contains...

Ngày tải lên: 07/08/2014, 15:22

... spectral radius of a general (not necessarily regular) graph G and that of a subgraph of G, see [16]. 2 The spectral radius and the maximum degree The following theorem is the main result of this ... to the extreme entries of the principal eigenvector of an irregular graph G, then one can improve the result of Theorem 2.1. However, there are infini...

Ngày tải lên: 07/08/2014, 15:22

... distance-regular if each vertex has at least one vertex at distance d and its distance-d adjacency matrix A d is a polynomial of degree d in the adjacency matrix A. This result is halfway towards the spectral ... distance-regular. This conclusion is the spectral excess theorem for this case. the electronic journal of combinatorics 15 (2008), #R129 4 The spectral excess...

Ngày tải lên: 07/08/2014, 21:20