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Completely Independent Spanning Trees in (Partial) k-Trees

Masayoshi Matsushita, Yota Otachi, Toru Araki (2015)

Discussiones Mathematicae Graph Theory

Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T1 and T2 are internally disjoint. For a graph G, we denote the maximum number of pairwise completely independent spanning trees by cist(G). In this paper, we consider cist(G) when G is a partial k-tree. First we show that [k/2] ≤ cist(G) ≤ k − 1 for any k-tree G. Then we show that for any p ∈ {[k/2], . . . , k − 1}, there exist infinitely many k-trees G such that cist(G)...

Complex Hadamard Matrices contained in a Bose–Mesner algebra

Takuya Ikuta, Akihiro Munemasa (2015)

Special Matrices

Acomplex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying HH* = nI, where * stands for the Hermitian transpose and I is the identity matrix of order n. In this paper, we first determine the image of a certain rational map from the d-dimensional complex projective space to Cd(d+1)/2. Applying this result with d = 3, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose–Mesner algebra of a certain 3-class symmetric...

Complexité et automates cellulaires linéaires

Valérie Berthé (2010)

RAIRO - Theoretical Informatics and Applications

The aim of this paper is to evaluate the growth order of the complexity function (in rectangles) for two-dimensional sequences generated by a linear cellular automaton with coefficients in ℤ / l ℤ , and polynomial initial condition. We prove that the complexity function is quadratic when l is a prime and that it increases with respect to the number of distinct prime factors of l.

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