منابع مشابه
Unimodular integer circulants
We study families of integer circulant matrices and methods for determining which are unimodular. This problem arises in the study of cyclically presented groups, and leads to the following problem concerning polynomials with integer coefficients: given a polynomial f(x) ∈ Z[x], determine all those n ∈ N such that Res(f(x), xn − 1) = ±1. In this paper we describe methods for resolving this prob...
متن کاملHuge tables are fixed parameter tractable via unimodular integer Caratheodory
The three-way table problem is to decide if there exists an l × m × n table satisfying given line sums, and find a table if yes. Recently, it was shown to be fixed-parameter tractable with parameters l, m. Here we extend this and show that the huge version of the problem, where the variable side n is encoded in binary, is also fixed-parameter tractable with parameters l, m. We also conclude tha...
متن کاملInteger Decomposition for Polyhedra Defined by Nearly Totally Unimodular Matrices
We call a matrix A nearly totally unimodular if it can be obtained from a totally unimodular matrix à by adding to each row of à an integer multiple of some fixed row a of Ã. For an integer vector b and a nearly totally unimodular matrix A, we denote by PA,b the integer hull of the set {x ∈ R | Ax ≤ b}. We show that PA,b has the integer decomposition property and that we can find a decompositio...
متن کاملLine Graphs and Circulants
The line graph of G, denoted L(G), is the graph with vertex set E(G), where vertices x and y are adjacent in L(G) iff edges x and y share a common vertex in G. In this paper, we determine all graphs G for which L(G) is a circulant graph. We will prove that if L(G) is a circulant, then G must be one of three graphs: the complete graph K4, the cycle Cn, or the complete bipartite graph Ka,b, for s...
متن کاملOn CIS circulants
A circulant is a Cayley graph over a cyclic group. A well-covered graph is a graph in which all maximal stable sets are of the same size α = α(G), or in other words, they are all maximum. A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. It is not difficult to show that a circulant G is a CIS graph if and only if G and its complement G are both well-co...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2008
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-08-02089-9