Note on edge-colored graphs and digraphs without properly colored cycles

We study the following two functions: d(n, c) and d(n, c); d(n, c) (d(n, c)) is the minimum number k such that every c-edge-colored undirected (directed) graph of order n and minimum monochromatic degree (out-degree) at least k has a properly colored cycle. Abouelaoualim et al. (2007) stated a conjecture

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Gregory Gutin
• Keywords: CORR 2007, Education, Minimum Monochromatic Degree, Minimum Number, Undirected