Contract grant sponsor: NSA; Contract grant number: MDA 904-03-1-0007; Contract grant sponsor: NSF; Contract grant number: DMS-0901520 (H. A. K.); Contract grant sponsor: NSF; Contract grant number: DMS-0965587; Contract grant sponsor: Russian Foundation for Basic Research; Contract grant number: 09-01-00244-a (A. V. K.).
Equitable List Coloring of Graphs with Bounded Degree
Article first published online: 10 DEC 2012
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 74, Issue 3, pages 309–334, November 2013
How to Cite
Kierstead, H. A. and Kostochka, A. V. (2013), Equitable List Coloring of Graphs with Bounded Degree. J. Graph Theory, 74: 309–334. doi: 10.1002/jgt.21710
- Issue published online: 5 SEP 2013
- Article first published online: 10 DEC 2012
- Manuscript Revised: 22 OCT 2012
- Manuscript Received: 6 JAN 2011
- NSA. Grant Number: MDA 904-03-1-0007
- NSF. Grant Number: DMS-0901520
- NSF. Grant Number: DMS-0965587
- Russian Foundation for Basic Research. Grant Number: 09-01-00244-a
- equitable coloring;
- list coloring;
- maximum degree
A graph G is equitably k-choosable if for every k-list assignment L there exists an L-coloring 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 -choosable. 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 -choosable. Our proofs yield polynomial algorithms for corresponding equitable list colorings.