On a minimum cycle basis of a graph
E. Kolasińska (1980)
Applicationes Mathematicae
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E. Kolasińska (1980)
Applicationes Mathematicae
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Gleiss, Petra M., Leydold, Josef, Stadler, Peter F. (2000)
The Electronic Journal of Combinatorics [electronic only]
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Walden, Byron L. (2005)
International Journal of Mathematics and Mathematical Sciences
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M.M.M. Jaradat (2008)
Discussiones Mathematicae Graph Theory
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A construction of minimum cycle bases of the lexicographic product of graphs is presented. Moreover, the length of a longest cycle of a minimal cycle basis is determined.
Al-Rhayyel, A.A. (1996)
International Journal of Mathematics and Mathematical Sciences
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Leydold, Josef, Stadler, Peter F. (1998)
The Electronic Journal of Combinatorics [electronic only]
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Hong Wang (2012)
Discussiones Mathematicae Graph Theory
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We prove that if G is a graph of order 5k and the minimum degree of G is at least 3k then G contains k disjoint cycles of length 5.
Stewart, Iain A., Thompson, Ben (1995)
Experimental Mathematics
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Petra M. Gleiss, Josef Leydold, Peter F. Stadler (2003)
Discussiones Mathematicae Graph Theory
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The cycle space of a strongly connected graph has a basis consisting of directed circuits. The concept of relevant circuits is introduced as a generalization of the relevant cycles in undirected graphs. A polynomial time algorithm for the computation of a minimum weight directed circuit basis is outlined.
Maciej Sysło (1982)
Banach Center Publications
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Fatima Affif Chaouche, Carrie G. Rutherford, Robin W. Whitty (2015)
Discussiones Mathematicae Graph Theory
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It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required. A possibly ‘intermediate’ variation is the following: given k, 1 ≤ k ≤ n, how many chords must be added to ensure that there exist cycles of every possible length each of which passes exactly k chords? For fixed k, we establish a lower bound of ∩(n1/k) on the growth rate.
Terry A. McKee (2012)
Discussiones Mathematicae Graph Theory
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A graph is edge cycle extendable if every cycle C that is formed from edges and one chord of a larger cycle C⁺ is also formed from edges and one chord of a cycle C' of length one greater than C with V(C') ⊆ V(C⁺). Edge cycle extendable graphs are characterized by every block being either chordal (every nontriangular cycle has a chord) or chordless (no nontriangular cycle has a chord); equivalently, every chord of a cycle of length five or more has a noncrossing chord.
John L. Simons (2008)
Acta Arithmetica
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Mohammed M.M. Jaradat (2006)
Discussiones Mathematicae Graph Theory
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A construction of a minimum cycle bases for the wreath product of some classes of graphs is presented. Moreover, the basis numbers for the wreath product of the same classes are determined.