{"id":{"repo_id":"wvu","oai_identifier":"oai:researchrepository.wvu.edu:etd-2011"},"canonical_url":"https://search.dev.ndltd.org/etd/wvu/oai:researchrepository.wvu.edu:etd-2011","repository":{"repo_id":"wvu","name":"West Virginia University","base_url":"https://researchrepository.wvu.edu/do/oai/"},"display":{"title":"Coloring clique hypergraphs","abstract":"Let G = (V, E) be a simple graph. The clique hypergraph of G, denoted as CH( G), has V as its set of vertices, and the maximal cliques as its hyperedges. Let Sk be a set of k colors. A map c : V Sk is a proper k-coloring for CH(G) if any maximal clique of G with at least two vertices receives at least two distinct colors. Let W ⊂ V, and let s ≥ 1. We say that G is (W, s)-extendible if any assignment on W with at most s colors can be extended to a proper s-coloring of CH(G). We prove that the clique hypergraphs of chordal and comparability graphs are bicolorable and that the clique hypergraphs of circular-arc graphs are 3-colorable. Our main result is the characterization of (W, 2)-extendibility for chordal graphs in the case when W=2 .","abstract_html":"Let G = (V, E) be a simple graph. The clique hypergraph of G, denoted as CH( G), has V as its set of vertices, and the maximal cliques as its hyperedges. Let Sk be a set of k colors. A map c : V Sk is a proper k-coloring for CH(G) if any maximal clique of G with at least two vertices receives at least two distinct colors. Let W ⊂ V, and let s ≥ 1. We say that G is (W, s)-extendible if any assignment on W with at most s colors can be extended to a proper s-coloring of CH(G). We prove that the clique hypergraphs of chordal and comparability graphs are bicolorable and that the clique hypergraphs of circular-arc graphs are 3-colorable. Our main result is the characterization of (W, 2)-extendibility for chordal graphs in the case when W=2 .","abstract_has_math":false,"creators":["Poon, Hoifung"],"institution":null,"degree_name":"MS","degree_level":"Thesis","degree_discipline":"Lane Department of Computer Science and Electrical Engineering","degree_department":null,"school":null,"contributors":["Elaine Eschen."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2000,"date_issued":"2000-08-01T07:00:00Z","date_published":"2000-08-01T07:00:00Z","updated_at":"2026-07-24T06:15:08Z","subjects":["Computer science","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://researchrepository.wvu.edu/etd/1008"],"render_values":[{"text":"https://researchrepository.wvu.edu/etd/1008","href":"https://researchrepository.wvu.edu/etd/1008","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.33915/etd.1008","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Elaine Eschen."]},{"key":"dc:creator","label":"Author","values":["Poon, Hoifung"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-01-17T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Lane Department of Computer Science and Electrical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computer science","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.33915/etd.1008","https://researchrepository.wvu.edu/etd/1008"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let G = (V, E) be a simple graph. The clique hypergraph of G, denoted as CH( G), has V as its set of vertices, and the maximal cliques as its hyperedges. Let Sk be a set of k colors. A map c : V Sk is a proper k-coloring for CH(G) if any maximal clique of G with at least two vertices receives at least two distinct colors. Let W ⊂ V, and let s ≥ 1. We say that G is (W, s)-extendible if any assignment on W with at most s colors can be extended to a proper s-coloring of CH(G). We prove that the clique hypergraphs of chordal and comparability graphs are bicolorable and that the clique hypergraphs of circular-arc graphs are 3-colorable. Our main result is the characterization of (W, 2)-extendibility for chordal graphs in the case when W=2 ."]},{"key":"dc:title","label":"Title","values":["Coloring clique hypergraphs"]}]}],"canonical_facts":{"dc:contributor":["Elaine Eschen."],"dc:creator":["Poon, Hoifung"],"dc:date.available":["2019-01-17T08:00:00Z"],"dc:description.abstract":["Let G = (V, E) be a simple graph. The clique hypergraph of G, denoted as CH( G), has V as its set of vertices, and the maximal cliques as its hyperedges. Let Sk be a set of k colors. A map c : V Sk is a proper k-coloring for CH(G) if any maximal clique of G with at least two vertices receives at least two distinct colors. Let W ⊂ V, and let s ≥ 1. We say that G is (W, s)-extendible if any assignment on W with at most s colors can be extended to a proper s-coloring of CH(G). We prove that the clique hypergraphs of chordal and comparability graphs are bicolorable and that the clique hypergraphs of circular-arc graphs are 3-colorable. Our main result is the characterization of (W, 2)-extendibility for chordal graphs in the case when W=2 ."],"dc:identifier":["https://doi.org/10.33915/etd.1008","https://researchrepository.wvu.edu/etd/1008"],"dc:subject":["Computer science","Mathematics"],"dc:title":["Coloring clique hypergraphs"],"thesis:degree_discipline":["Lane Department of Computer Science and Electrical Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T06:15:08Z"}