Báo cáo toán học: "Random Cayley graphs are expanders: a simple proof of the Alon–Roichman theorem" potx

... journal of combinatorics 11 (2004), #R62 3 Random Cayley graphs are expanders: a simple proof of the Alon–Roichman theorem ZEPH LANDAU Department of Mathematics City College of New York landau@sci.ccny.cuny.edu A LEXANDER ... it establishes the result above with a smaller constant c ε . 1 Introduction A beautiful theorem of N. Alon and Y. Roichman [4] asser...

Ngày tải lên: 07/08/2014, 08:20

... integral? A. Abdollahi Department of Mathematics University of Isfahan Isfahan 81746-73441 Iran a. abdollahi@math.ui.ac.ir E. Vatandoost Department of Mathematics University of Isfahan Isfahan 81746-73441 Iran e.vatandoost@math.ui.ac.ir Submitted: ... infinite family of connected integ r al Cayley graphs. The main results are the following. Theorem 1.1 There are exactly...

Ngày tải lên: 08/08/2014, 01:20

... journal of combinatorics 12 (2005), #R18 4 A Simple Proof of the Aztec Diamond Theorem Sen-Peng Eu ∗ Department of Applied Mathematics National University of Kaohsiung Kaohsiung 811, Taiwan, ROC speu@nuk.edu.tw Tung-Shan ... Classifications: 0 5A1 5; 05B45; 05C50; 05C20 Abstract Based on a bijection between domino tilings of an Aztec diamond and non- intersecting lattice pa...

Ngày tải lên: 07/08/2014, 08:22

... so-called vertex guards. Their proof is based upon quadrilateral- ization and a 4-coloring of the resultant quadrilateralization graph. Let us recall that a quadrilateralization of an orthogonal ... to the edges of polygon P , to the diagonals of quadrilateralization Q, and to the added internal diagonals of all quadrilaterals, as depicted in Fig. 3. Our goal is to 4-c...

Ngày tải lên: 07/08/2014, 13:21

... β c on the square and tr ia ngular lat t ices. Marek Biskup, Roman Koteck´y, and Senya Shlosman kindly proposed the proof of the continuity at β c of the Ising magnetization. We thank Jakob Bj¨or ... literature, and physicists have a detailed knowledge of the two-dimensional case particularly. There is a host of ‘exact calculations’, rigorous proofs of which can pres...

Ngày tải lên: 07/08/2014, 21:21

... 2007. [2] Andreas Brandst¨adt, Van Ban Le, and Jeremy Spinrad. Graph Classes: A Survey. SIAM, 1999. [3] Robert Brawer and Magnus Pirovino. The linear algebra of the Pascal matrix. Linear Algebra and ... cannot be the common element of A and B (because we are not in case (a) of the proof of Theorem 5.30). So there are h − 1 choices for the intersection a α = b β ....

Ngày tải lên: 08/08/2014, 01:20

... α  as there are α + β − 2 elements of A ∪ B smaller than a α = b β (and we put α − 1 in A and the others in B) and there are 2h − α − β elements of A ∪ B greater than a α = b β . To calculate the ... cannot be the common element of A and B (because we are not in case (a) of the proof of Theorem 5.30). So there are h − 1 choices for the intersection...

Ngày tải lên: 08/08/2014, 11:20

... are proven to be int egra l Cayley graphs, which extends a partial result in [14]. Moreover, we show that certain graphs associated with the Sudoku puzzle and with pandiagonal Latin squares are ... For a pandiagonal Latin square two additional conditions have to be satisfied. Every number 1, . . ., n has to appear exactly once in the main diagonal and its broken parallels as w...

Ngày tải lên: 08/08/2014, 12:22

... integral, if all of its eigenvalues are integers. For a survey of integral graphs see [3]. In [2] the numb er of integral graphs on n vertices is estimated. Known characterizations of integral graphs ... Which graphs have integral spectra? Lecture Notes in Mathematics 406, Springer Verlag (1974), 45–50 . [9] Ili ´ c, A. The energy of unitary cayley graphs. Linear...

Ngày tải lên: 08/08/2014, 14:23

... γ. The elements of Γ are called basic relations, their graphs basic graphs, and the numbers p γ α,β are called the structure constants of the coherent configuration (X;Γ). For any relation γ ∈ Γandapointx ... can be numbered in such a way that the resulting adjacency matrix A( G) is a circulant matrix. We call such a numbering a Cayley num- bering. Still another...

Ngày tải lên: 07/08/2014, 06:22