Chromatic number of graphs with special distance sets, I
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Chromatic number of graphs with special distance sets, I
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| Creator |
Yegnanarayanan, V.
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| Description |
Given a subset D of positive integers, an integer distance graph is a graph G(Z, D) with the set Z of integers as vertex set and with an edge joining two vertices u and v if and only if |u−v| ∈ D. In this paper we consider the problem of determining the chromatic number of certain integer distance graphs G(Z, D)whose distance set D is either 1) a set of (n + 1) positive integers for which the nth power of the last is the sum of the nth powers of the previous terms, or 2) a set of pythagorean quadruples, or 3) a set of pythagorean n-tuples, or 4) a set of square distances, or 5) a set of abundant numbers or deficient numbers or carmichael numbers, or 6) a set of polytopic numbers, or 7) a set of happy numbers or lucky numbers, or 8) a set of Lucas numbers, or 9) a set of Ulam numbers, or 10) a set of weird numbers. Besides finding the chromatic number of a few specific distance graphs we also give useful upper and lower bounds for general cases. Further, we raise some open problems.
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| Date |
2019-06-10T11:10:25Z
2019-06-10T11:10:25Z 2014 |
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| Type |
Article
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| Identifier |
Chromatic number of graphs with special distance sets, I / V. Yegnanarayanan // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 1. — С. 135–160. — Бібліогр.: 59 назв. — англ.
1726-3255 2010 MSC:05C15. http://dspace.nbuv.gov.ua/handle/123456789/152354 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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