On a minimum cycle basis of a graph
E. Kolasińska (1980)
Applicationes Mathematicae
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Displaying similar documents to “Union of all the minimum cycle bases of a graph.”
On a minimum cycle basis of a graph
Interchangeability of relevant cycles in graphs.
Gleiss, Petra M., Leydold, Josef, Stadler, Peter F. (2000)
The Electronic Journal of Combinatorics [electronic only]
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Searching for Kaprekar's constants: algorithms and results.
Walden, Byron L. (2005)
International Journal of Mathematics and Mathematical Sciences
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Minimal cycle bases of the lexicographic product of graphs
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.
On the basis of the direct product of paths and wheels.
Al-Rhayyel, A.A. (1996)
International Journal of Mathematics and Mathematical Sciences
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Minimal cycle bases of outerplanar graphs.
Leydold, Josef, Stadler, Peter F. (1998)
The Electronic Journal of Combinatorics [electronic only]
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Disjoint 5-cycles in a graph
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.
On the intersections of longest cycles in a graph.
Stewart, Iain A., Thompson, Ben (1995)
Experimental Mathematics
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Circuit bases of strongly connected digraphs
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.
On some problem related to fundamental cycle sets of a graph: Research notes
Maciej Sysło (1982)
Banach Center Publications
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Pancyclicity when each Cycle Must Pass Exactly k Hamilton Cycle Chords
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.
Edge cycle extendable graphs
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.
Exotic Collatz cycles
John L. Simons (2008)
Acta Arithmetica
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On the basis number and the minimum cycle bases of the wreath product of some graphs i
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.