Positive graphs

Omar Antolín Camarena, Endre Csóka, Tamás Hubai, Gábor Lippner, László Lovász

Research output: Contribution to journalArticle

2 Citations (Scopus)


We study "positive" graphs that have a nonnegative homomorphism number into every edge-weighted graph (where the edgeweights may be negative). We conjecture that all positive graphs can be obtained by taking two copies of an arbitrary simple graph and gluing them together along an independent set of nodes. We prove the conjecture for various classes of graphs including all trees. We prove a number of properties of positive graphs, including the fact that they have a homomorphic image which has at least half the original number of nodes but in which every edge has an even number of pre-images. The results, combined with a computer program, imply that the conjecture is true for all but one graph up to 10 nodes.

Original languageEnglish
Pages (from-to)290-301
Number of pages12
JournalEuropean Journal of Combinatorics
Publication statusPublished - Feb 1 2016

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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    Antolín Camarena, O., Csóka, E., Hubai, T., Lippner, G., & Lovász, L. (2016). Positive graphs. European Journal of Combinatorics, 52, 290-301. https://doi.org/10.1016/j.ejc.2015.07.007