11 papers
Reconfiguration of Nowhere-zero Flows
Daniel W. Cranston, Jiaao Li, Bo Su +2
Fix an abelian group , a graph , and nowhere-zero -flows and on . Now and are \emph{-flow-adjacent} if there exists a cycle in such tha…
Coloring, List Coloring, and Painting Squares of Graphs (and other related problems)
Daniel W. Cranston
We survey work on coloring, list coloring, and painting squares of graphs; in particular, we consider strong edge-coloring. We focus primarily on planar graphs and other sparse cla…
Orientations of -Edge-Connected Planar Multigraphs and Applications
Daniel W. Cranston, Jiaao Li, Bo Su +2
A graph is called strongly -connected if for each boundary function with , there exists an orientatio…
Disjoint Correspondence Colorings for -Minor-free Graphs
Wouter Cames van Batenburg, Daniel W. Cranston, František Kardoš
Thomassen famously proved that every planar graph is 5-choosable. We explore variants of this result, focusing on finding disjoint correspondence colorings, in the more general cla…
Progress on Albertson's Conjecture
Daniel W. Cranston
Albertson conjectured that every graph with chromatic number has crossing number at least the crossing number of the complete graph . This conjecture was proved for $r\le…
Equitably Coloring Planar and Outerplanar Graphs
Daniel W. Cranston, Reem Mahmoud
A proper -coloring of an -vertex graph is \emph{equitable} if every color class has size or . A necessary condition to have an equita…