We consider two branches of coloring problems for graphs: list coloring and packing coloring. We introduce a new variation to list coloring which we call choosability with union separation: For a graph G, a list assignment L to the vertices of G is a (k,k+t)-list assignment if every vertex is assigned a list of size at least k and the union of the lists of each pair of adjacent vertices is at least k+t. We explore this new variation and offer comparative results to choosability with intersection separation, a variation that has been studied previously.
Regarding packing colorings, we consider infinite lattice graphs and provide bounds to their packing chromatic numbers. We also provide algorithms for coloring these graphs. The lattices we color include two-layer hexagonal lattices as well as the truncated square lattice, a 3-regular lattice whose faces have length 4 and 8.
","abstract_html":"<p>We consider two branches of coloring problems for graphs: list coloring and packing coloring. We introduce a new variation to list coloring which we call choosability with union separation: For a graph G, a list assignment L to the vertices of G is a (k,k+t)-list assignment if every vertex is assigned a list of size at least k and the union of the lists of each pair of adjacent vertices is at least k+t. We explore this new variation and offer comparative results to choosability with intersection separation, a variation that has been studied previously.</p> <p>Regarding packing colorings, we consider infinite lattice graphs and provide bounds to their packing chromatic numbers. We also provide algorithms for coloring these graphs. The lattices we color include two-layer hexagonal lattices as well as the truncated square lattice, a 3-regular lattice whose faces have length 4 and 8.</p>","abstract_has_math":false,"creators":["Moss, Kevin"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"dissertation","degree_discipline":"Mathematics","degree_department":"Department of Mathematics","school":null,"contributors":[],"advisors":["Berard Lidicky","Steve Butler"],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-01-01","date_published":"2017-01-01","updated_at":"2026-07-24T02:38:46Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.31274/etd-180810-5276"],"render_values":[{"text":"https://doi.org/10.31274/etd-180810-5276","href":"https://doi.org/10.31274/etd-180810-5276","code":true}]},{"key":"dc:identifier","label":"Identifier","values":["archive/lib.dr.iastate.edu/etd/15383/"],"render_values":[{"text":"archive/lib.dr.iastate.edu/etd/15383/","href":null,"code":true}]}]},"links":{"outbound_url":"https://dr.lib.iastate.edu/handle/20.500.12876/29566","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Berard Lidicky","Steve Butler"]},{"key":"dc:contributor.department","label":"Department","values":["Department of Mathematics"]},{"key":"dc:creator","label":"Author","values":["Moss, Kevin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-08-11T06:22:00.000"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-06-30T03:03:30Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-06-30T03:03:30Z"]},{"key":"dc:date.issued","label":"Date","values":["2017-01-01"]},{"key":"dc:type","label":"Dc Type","values":["dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["archive/lib.dr.iastate.edu/etd/15383/"]},{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.31274/etd-180810-5276"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://dr.lib.iastate.edu/handle/20.500.12876/29566"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We consider two branches of coloring problems for graphs: list coloring and packing coloring. We introduce a new variation to list coloring which we call choosability with union separation: For a graph G, a list assignment L to the vertices of G is a (k,k+t)-list assignment if every vertex is assigned a list of size at least k and the union of the lists of each pair of adjacent vertices is at least k+t. We explore this new variation and offer comparative results to choosability with intersection separation, a variation that has been studied previously.
Regarding packing colorings, we consider infinite lattice graphs and provide bounds to their packing chromatic numbers. We also provide algorithms for coloring these graphs. The lattices we color include two-layer hexagonal lattices as well as the truncated square lattice, a 3-regular lattice whose faces have length 4 and 8.
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Regarding packing colorings, we consider infinite lattice graphs and provide bounds to their packing chromatic numbers. We also provide algorithms for coloring these graphs. The lattices we color include two-layer hexagonal lattices as well as the truncated square lattice, a 3-regular lattice whose faces have length 4 and 8.
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