Let G be an edge-colored graph. The minimum color degree δc(G) of G is the largest integer k such that for every vertex ν, there are at least k distinct colors on edges incident to ν. We say that G is properly colored if no two adjacent edges have the same color. In this paper, we show that every edge-colored graph G with δc(G) ≥ 2|G|/3 contains a properly colored 2-factor. Furthermore, we show that for any ε > 0 there exists an integer n0 such that every edge-colored graph G with |G| = n ≥ n0 and δc(G) ≥ (2/3 + ε)n contains a properly colored cycle of length ℓ for every 3 ≤ ℓ ≤ n. This result is best possible in the sense that the statement is false for δc(G) < 2n/3.
|Number of pages||19|
|Journal||SIAM Journal on Discrete Mathematics|
|Publication status||Published - 2 Jan 2014|
- Hamiltonian cycle
- Proper edge-coloring
ASJC Scopus subject areas