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Displaying similar documents to “A Note on a Broken-Cycle Theorem for Hypergraphs”

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.

Decomposition of Complete Multigraphs Into Stars and Cycles

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.