{"paper":{"title":"Hedetniemi's Conjecture Via Altermatic Number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hossein Hajiabolhassan, Meysam Alishahi","submitted_at":"2014-03-18T11:04:57Z","abstract_excerpt":"A $50$ years unsolved conjecture by Hedetniemi [{\\it Homomorphisms of graphs and automata, \\newblock {\\em Thesis (Ph.D.)--University of Michigan}, 1966}] asserts that the chromatic number of the categorical product of two graphs $G$ and $H$ is $\\min\\{\\chi(G),\\chi(H)\\}$. The present authors [{\\it On the chromatic number of general {K}neser hypergraphs. \\newblock {\\em Journal of Combinatorial Theory, Series B}, 2015.}] introduced the altermatic and the strong altermatic number of graphs as two tight lower bounds for the chromatic number of graphs. In this work, we prove a relaxation of Hedetniem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4404","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}