Chorded Cycles |
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| Authors: | Megan Cream Ralph J Faudree Ronald J Gould Kazuhide Hirohata |
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| Institution: | 1.Spelman College,Atlanta,USA;2.University of Memphis,Memphis,USA;3.Emory University,Atlanta,USA;4.National Institute of Technology,Ibaraki College,Ibaraki,Japan |
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| Abstract: | A chord is an edge between two vertices of a cycle that is not an edge on the cycle. If a cycle has at least one chord, then the cycle is called a chorded cycle, and if a cycle has at least two chords, then the cycle is called a doubly chorded cycle. The minimum degree and the minimum degree-sum conditions are given for a graph to contain vertex-disjoint chorded (doubly chorded) cycles containing specified elements of the graph, i.e., specified vertices, specified edges as cycle-edges, specified paths, or specified edges as chords. Furthermore, the minimum degree condition is given for a graph to be partitioned into chorded cycles containing specified edges as cycle-edges. |
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