Abstract
AbstractA graph G is equitably kâchoosable if for every kâlist assignment L there exists an Lâcoloring of G such that every color class has at most vertices. We prove results toward the conjecture that every graph with maximum degree at most r is equitably âchoosable. In particular, we confirm the conjecture for and show that every graph with maximum degree at most r and at least r3 vertices is equitably âchoosable. Our proofs yield polynomial algorithms for corresponding equitable list colorings.
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