Positivity of three-term recurrence sequences.
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Liu, Lily L. (2010)
The Electronic Journal of Combinatorics [electronic only]
Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson (2005)
Discussiones Mathematicae Graph Theory
In [1], Brousek characterizes all triples of connected graphs, G₁,G₂,G₃, with for some i = 1,2, or 3, such that all G₁G₂ G₃-free graphs contain a hamiltonian cycle. In [8], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G₁,G₂,G₃, none of which is a , s ≥ 3 such that G₁G₂G₃-free graphs of sufficiently large order contain a hamiltonian cycle. In [6], a characterization was given of all triples G₁,G₂,G₃ with none being , such that all G₁G₂G₃-free graphs are...
Michael Ferrara, Michael Jacobson, John Schmitt, Mark Siggers (2009)
Discussiones Mathematicae Graph Theory
We extend the notion of a potentially H-graphic sequence as follows. Let A and B be nonnegative integer sequences. The sequence pair S = (A,B) is said to be bigraphic if there is some bipartite graph G = (X ∪ Y,E) such that A and B are the degrees of the vertices in X and Y, respectively. If S is a bigraphic pair, let σ(S) denote the sum of the terms in A. Given a bigraphic pair S, and a fixed bipartite graph H, we say that S is potentially H-bigraphic if there is some realization of S containing...
Chunhui Lai, Lili Hu (2009)
Czechoslovak Mathematical Journal
The set of all non-increasing nonnegative integer sequences () is denoted by . A sequence is said to be graphic if it is the degree sequence of a simple graph on vertices, and such a graph is called a realization of . The set of all graphic sequences in is denoted by . A graphical sequence is potentially -graphical if there is a realization of containing as a subgraph, while is forcibly -graphical if every realization of contains as a subgraph. Let denote a complete...
R. Brawer (1990)
Elemente der Mathematik
Jaroslav Březina (1973)
Matematický časopis
Bo Zhou (2004)
Discussiones Mathematicae - General Algebra and Applications
The power index of a square Boolean matrix A is the least integer d such that Ad is a linear combination of previous nonnegative powers of A. We determine the maximum power indices for the class of n×n primitive symmetric Boolean matrices of trace zero, the class of n×n irreducible nonprimitive symmetric Boolean matrices, and the class of n×n reducible symmetric Boolean matrices of trace zero, and characterize the extreme matrices respectively.
Louck, James D. (1999)
International Journal of Mathematics and Mathematical Sciences
Mc Laughlin, J., Sury, B. (2005)
Integers
Alexander Rosa (1966)
Matematicko-fyzikálny časopis
Václav Havel (1955)
Časopis pro pěstování matematiky
Oleg V. Borodin (1992)
Mathematica Slovaca
Donald W. Crowe (1999)
Visual Mathematics
Oleg V. Borodin, Anna O. Ivanova (2013)
Discussiones Mathematicae Graph Theory
We prove that every planar graph with maximum degree ∆ is strong edge (2∆−1)-colorable if its girth is at least 40 [...] +1. The bound 2∆−1 is reached at any graph that has two adjacent vertices of degree ∆.
Hujter, M., Tuza, Zs. (1993)
Acta Mathematica Universitatis Comenianae. New Series
Kratochvíl, J. (1993)
Acta Mathematica Universitatis Comenianae. New Series
Jaggard, Aaron D. (2003)
The Electronic Journal of Combinatorics [electronic only]
J. Higgins, D. Campbell (1993)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
Somayeh Bandari, Kamran Divaani-Aazar, Ali Soleyman Jahan (2014)
Czechoslovak Mathematical Journal
Let be a field and . Let be a monomial ideal of and be monomials in . We prove that if form a filter-regular sequence on , then is pretty clean if and only if is pretty clean. Also, we show that if form a filter-regular sequence on , then Stanley’s conjecture is true for if and only if it is true for . Finally, we prove that if is a minimal set of generators for which form either a -sequence, proper sequence or strong -sequence (with respect to the reverse lexicographic...
Sofia Kovaleva, Frits C. R. Spieksma (2002)
RAIRO - Operations Research - Recherche Opérationnelle
We consider a special packing-covering pair of problems. The packing problem is a natural generalization of finding a (weighted) maximum independent set in an interval graph, the covering problem generalizes the problem of finding a (weighted) minimum clique cover in an interval graph. The problem pair involves weights and capacities; we consider the case of unit weights and the case of unit capacities. In each case we describe a simple algorithm that outputs a solution to the packing problem and...