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arXiv · 1312.1880

Path coverings with prescribed ends in faulty hypercubes

Nelson Castañeda·Ivan S. Gotchev
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Abstract

We discuss the existence of vertex disjoint path coverings with prescribed ends for the $n$-dimensional hypercube with or without deleted vertices. Depending on the type of the set of deleted vertices and desired properties of the path coverings we establish the minimal integer $m$ such that for every $n \ge m$ such path coverings exist. Using some of these results, for $k \le 4$, we prove Locke's conjecture that a hypercube with $k$ deleted vertices of each parity is Hamiltonian if $n \ge k +2.$ Some of our lemmas substantially generalize known results of I. Havel and T. Dvořák. At the end of the paper we formulate some conjectures supported by our results.

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Nelson Castañeda, Ivan S. Gotchev. 2013-12-06. Path coverings with prescribed ends in faulty hypercubes. https://arxiv.org/abs/1312.1880

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