Powers of Hamiltonian paths in interval graphs
نویسندگان
چکیده
منابع مشابه
Powers of Hamiltonian paths in interval graphs
We give a simple proof that the obvious necessary conditions for a graph to contain the kth power of a Hamiltonian path are sufficient for the class of interval graphs. The proof is based on showing that a greedy algorithm tests for the existence of Hamiltonian path powers in interval graphs. We will also discuss covers by powers of paths and analogues of the Hamiltonian completion number. c © ...
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The vertex set of the k cartesian power of a directed cycle of length m can be naturally identified with the abelian group (Zm) . For any two elements v = (v1, . . . , vk) and w = (w1, . . . , wk) of (Zm) , it is easy to see that if there is a hamiltonian path from v to w, then v1 + · · ·+ vk ≡ w1 + · · ·+ wk + 1 (mod m). We prove the converse, unless k = 2 and m is odd.
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 1998
ISSN: 0364-9024,1097-0118
DOI: 10.1002/(sici)1097-0118(199805)28:1<31::aid-jgt3>3.0.co;2-g