%0 Journal Article
%T The Erdös-Faber-Lovász Conjecture for Gap-Restricted Hypergraphs
%A Zhimin Wang
%J Engineering
%P 47-59
%@ 1947-394X
%D 2024
%I Scientific Research Publishing
%R 10.4236/eng.2024.162006
%X An edge coloring of hypergraph <i>H</i> is a function&nbsp;<img src=\"Edit_122f1086-a758-47fe-bc1c-c37f8cab239e.png\" alt=\"\" />&nbsp;<span style=\"color:black;\"><span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><span> </span><span>such that&nbsp;<img src=\"Edit_aad8c7c9-f672-4ac4-a8b4-027dc4a53962.png\" alt=\"\" />&nbsp;</span></span><span style=\"color:black;\"><span></span></span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><span></span>holds for any pair of intersecting edges <img src=\"Edit_bf638468-4846-4886-8540-a435d8c656da.png\" alt=\"\" /></span><span style=\"color:black;\"><span></span></span></span></span><span><span><span style=\"font-family:;\" \"=\"\">.</span></span></span><span><span><span style=\"font-family:;\" \"=\"\"> <span>The minimum number of colors in edge
colorings of <i>H</i> is called the chromat</span>ic
index of <i>H</i> and is denoted by <img src=\"Edit_bfbc1320-7399-4b09-b8b0-1612710f1764.png\" alt=\"\" /></span><span style=\"color:black;\"><span></span></span></span></span><span><span><span style=\"font-family:;\" \"=\"\">. Erd<span style=\"font-family:Verdana, Helvetica, Arial;text-wrap:wrap;background-color:#FFFFFF;\">&amp;ouml;</span>s, Faber and Lov¨¢sz proposed a famous
conjecture that&nbsp;<img src=\"Edit_66ff7d0f-04f0-413b-b098-3d4636473d04.png\" alt=\"\" />&nbsp;</span><span style=\"color:black;\"><span></span></span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><span></span>holds for any
loopless linear hypergraph <i><span>H</span></i><span> with <i>n</i> vertices. In this paper, we show
that&nbsp;<img src=\"Edit_390e86ea-d03e-4220-9bcd-bda4051031c9.png\" alt=\"\" />&nbsp;</span></span><span style=\"color:black;\"><span></span></span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><span></span>is true for gap-</span></span></span><span><span><span style=\"font-family:;\" \"=\"\">restricted hypergraphs. Our result extends a result of Alesandroni in
2021.</span></span></span>
%K Linear Hypergraph
%K Chromatic Index
%K Erd&#246
%K s-Faber-Lov&#225
%K sz Conjecture
%K Edge Cardinality
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=131562