Colorings of (r, r)-Uniform, Complete, Circular, Mixed Hypergraphs

Nicholas Newman and Vitaly Voloshin
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Nicholas Newman: Department of Mathematics and Statistics, Troy University, 600 University Ave., Troy, AL 36082, USA
Vitaly Voloshin: Department of Mathematics and Statistics, Troy University, 600 University Ave., Troy, AL 36082, USA

Mathematics, 2021, vol. 9, issue 8, 1-5

Abstract: In colorings of some block designs, the vertices of blocks can be thought of as hyperedges of a hypergraph H that can be placed on a circle and colored according to some rules that are related to colorings of circular mixed hypergraphs. A mixed hypergraph H is called circular if there exists a host cycle on the vertex set X such that every edge ( C - or D -) induces a connected subgraph of this cycle. We propose an algorithm to color the ( r , r ) -uniform, complete, circular, mixed hypergraphs for all feasible values with no gaps. In doing so, we show ? ( H ) = 2 and ? ¯ ( H ) = n ? s or n ? s ? 1 where s is the sieve number.

Keywords: coloring; circular; mixed hypergraphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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