document: Edge-colorings with no large polychromatic stars Given a graph G and a positive integer r , let f/sub r / -LRB- G -RRB- denote the largest number of colors that can be used in a coloring of E -LRB- G -RRB- such that each vertex is incident to at most r colors . For all positive integers n and r , we determine f/sub r / -LRB- K/sub n , n / -RRB- exactly and f/sub r / -LRB- K/sub n / -RRB- within 1 . In doing so , we disprove a conjecture by Y. Manoussakis et al. -LRB- 1996 -RRB-
doc_bio_tags: O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: polychromatic stars positive integer positive integers
abstractive_keyphrases: edge colorings