Some gregarious cycle decompositions of complete equipartite graphs.
Smith, Benjamin R. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Smith, Benjamin R. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Jordon, Heather (2011)
The Electronic Journal of Combinatorics [electronic only]
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Bernhardt, Chris (2003)
International Journal of Mathematics and Mathematical Sciences
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Fairouz Beggas, Mohammed Haddad, Hamamache Kheddouci (2015)
Discussiones Mathematicae Graph Theory
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Let k be a positive integer, Sk and Ck denote, respectively, a star and a cycle of k edges. λKn is the usual notation for the complete multigraph on n vertices and in which every edge is taken λ times. In this paper, we investigate necessary and sufficient conditions for the existence of the decomposition of λKn into edges disjoint of stars Sk’s and cycles Ck’s.
Eckhard Steffen (2001)
Mathematica Slovaca
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Ruskey, F., Sawada, Joe (2003)
The Electronic Journal of Combinatorics [electronic only]
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John L. Simons (2008)
Acta Arithmetica
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Gleiss, Petra M., Leydold, Josef, Stadler, Peter F. (2000)
The Electronic Journal of Combinatorics [electronic only]
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Al-Rhayyel, A.A. (1996)
International Journal of Mathematics and Mathematical Sciences
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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.
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.
Bernhardt, Chris (2003)
International Journal of Mathematics and Mathematical Sciences
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