Minimal Degree and (k, m)-Pancyclic Ordered Graphs

Given positive integers k less than or equal to m less than or equal to 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 less than or equal to r less than or equal to n, there is a cycle of length r encountering the k vertices in a specifi...

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Published in:Graphs and combinatorics 2005-06, Vol.21 (2), p.197-211
Main Authors: Faudree, Ralph J., Gould, Ronald J., Jacobson, Michael S., Lesniak, Linda
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Language:English
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Graph algorithms
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creator Faudree, Ralph J.
Gould, Ronald J.
Jacobson, Michael S.
Lesniak, Linda
description Given positive integers k less than or equal to m less than or equal to 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 less than or equal to r less than or equal to 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. [PUBLICATION ABSTRACT]
doi_str_mv 10.1007/s00373-005-0604-5
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title Minimal Degree and (k, m)-Pancyclic Ordered Graphs
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