Minimal Degree and (k, m)-Pancyclic Ordered Graphs |
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| Authors: | Ralph J. Faudree Ronald J. Gould Michael S. Jacobson Linda Lesniak |
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| Affiliation: | (1) Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA;(2) Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA;(3) Department of Mathematics, University of Colorado at Denver, Denver, CO, 80217, USA;(4) Department of Mathematics, Drew University, Madison, NJ 07940, USA |
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| Abstract: | Given positive integers k  m n, a graph G of order n is (k, m)-pancyclic ordered if for any set of k vertices of G and any integer r with m r n, there is a cycle of length r encountering the k vertices in a specified order. Minimum degree conditions that imply a graph of sufficiently large order n is (k, m)-pancylic ordered are proved. Examples showing that these constraints are best possible are also provided. |
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