K e y w o r d s L i s t improper coloring, List chromatic number, Cycles. 1. I N T R O D U C T I O N All g r aphs cons idered in th i s pape r are finite, loopless, and w i thou t mul t ip le edgesâ€¦ (More)

A setS of vertices of the graphG is calledk-reducibleif the following is true:G is k-choosable if and only if G âˆ’ S is k-choosable. Ak-reduced subgraphH of G is a subgraph of G such thatH containsâ€¦ (More)

The coupled graph c(G) of a plane graph G is the graph de.ned on the vertex set V (G)âˆªF(G) so that two vertices in c(G) are joined by an edge if and only if they are adjacent or incident in G. Weâ€¦ (More)