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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The authors would like to thank the referees for their helpful comments and suggestions.
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M. Cream, R. Gould, and K. Hirohata would like to dedicate this paper to the memory of our colleague and friend, Ralph J. Faudree.
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Cream, M., Faudree, R.J., Gould, R.J. et al. Chorded Cycles. Graphs and Combinatorics 32, 2295–2313 (2016). https://doi.org/10.1007/s00373-016-1729-4
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DOI: https://doi.org/10.1007/s00373-016-1729-4