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Acyclic 4-choosability of planar graphs without 4-cycles

Yingcai SunMin Chen — 2020

Czechoslovak Mathematical Journal

A proper vertex coloring of a graph G is acyclic if there is no bicolored cycle in G . In other words, each cycle of G must be colored with at least three colors. Given a list assignment L = { L ( v ) : v V } , if there exists an acyclic coloring π of G such that π ( v ) L ( v ) for all v V , then we say that G is acyclically L -colorable. If G is acyclically L -colorable for any list assignment L with | L ( v ) | k for all v V , then G is acyclically k -choosable. In 2006, Montassier, Raspaud and Wang conjectured that every planar graph without 4-cycles...

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