Replication in critical graphs and the persistence of monomial ideals |
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| Authors: | Tomá &scaron Kaiser,Matěj Stehlí k,Riste &Scaron krekovski |
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| Affiliation: | 1. Department of Mathematics, Institute for Theoretical Computer Science (CE-ITI) and European Centre of Excellence NTIS—New Technologies for Information Society, University of West Bohemia, Univerzitní 8, 306 14 Plzeň, Czech Republic;2. UJF-Grenoble 1/CNRS/Grenoble-INP, G-SCOP UMR5272, Grenoble, F-38031, France;3. Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia;4. Faculty of Information Studies, Novo Mesto, Slovenia;5. FAMNIT, University of Primorska, Koper, Slovenia |
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| Abstract: | Motivated by questions about square-free monomial ideals in polynomial rings, in 2010 Francisco et al. conjectured that for every positive integer k and every k-critical (i.e., critically k -chromatic) graph, there is a set of vertices whose replication produces a (k+1)-critical graph. (The replication of a set W of vertices of a graph is the operation that adds a copy of each vertex w in W, one at a time, and connects it to w and all its neighbours.) |
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| Keywords: | Critical graph Replication Cover ideal Square-free monomial ideal Associated prime Persistence property |
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