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This article is available for purchase or by subscription. See below.
Abstract
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We establish the complexity of recognizing
-distance
graphs and estimating the chromatic number of the real line with a set of forbidden distances
, where
the set
is
a collection of elements of a geometric progression with the common
ratio equal to a rational number raised to a rational power. For all
sets of
this type we have found the chromatic number of the real line with this set of forbidden
distances and proved whether the problem of recognizing nonstrictly noninjectively
-embeddable-in-
graphs is polynomial or NP-hard.
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Keywords
distance graph, chromatic number, computation complexity
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Mathematical Subject Classification
Primary: 05C15, 68Q17
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Milestones
Received: 7 July 2023
Accepted: 7 August 2023
Published: 23 September 2023
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Publishers). |
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