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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Effective matchmaking and $ k$-chromatic graphs


Authors: Alfred B. Manaster and Joseph G. Rosenstein
Journal: Proc. Amer. Math. Soc. 39 (1973), 371-378
MSC: Primary 05C15; Secondary 02F50
MathSciNet review: 0340082
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Abstract: In an earlier paper we showed that there is a recursive society, in which each person knows exactly two other people, whose marriage problem is solvable but not recursively solvable. We generalize this result, using a different construction, to the case where each person knows exactly $ k$ other people. From this we deduce that for each $ k \geqq 2$ there is a recursive $ 2(k - 1)$-regular graph, whose chromatic number is $ k$ but which is not recursively $ k$ chromatic.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0340082-2
Keywords: Bipartite graph, $ k$-regular graph, chromatic number, matching, marriage problem, algorithm, recursive function
Article copyright: © Copyright 1973 American Mathematical Society