... resultant quadrilateralization graph. Let us recall that a
quadrilateralization of an orthogonal polygon P (with or without holes) is a partitioning
of P into a set of convex quadrilaterals with pairwise ... Orthogonal galleries with one hole
Let Q be a quadrilateralization of an n-vertex orthogonal polygon P with one hole. By
adding both diagonals to each quadrilater...
... 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 ... adjacency matrix of the graph is less than ε as long as k ≥ (c
ε
+ o(1)) log |G|. Their proof
involves a clever combinatorial argument that controls...
... described each of the arrays A
s
as
endowing N
0
with the algebraic structure of a quasigroup [22]. We discuss results
related to this algebraic approach in [1]; that article deals with the same family ... operation of Nim-
addition. In particular, these arrays display periodic behavior along rows and
diagonals. We explain how various features of computer-generated graphics
de...
... from a set S that contains s symbols is said to be an
orthogonal array with s levels, strength t and index λ if every N ×t subarray of A contains
∗
Osaka prefectual Nagano high school, 1-1-2 Hara, ... Hara, Kawachinagano, Osaka, Japan,
e-mail; denen482@yahoo.co .jp
the electronic journal of combinatorics 18 (2011), #P69 1
PROOF. From Lemmas A, B, C and the theorem of Veblen and...