05964678

j

05964678 Fujita, Shinya Magnant, Colton Properly colored paths and cycles. Discrete Appl. Math. 159, No. 14, 1391-1397 (2011). 2011 Elsevier Science B.V. (North-Holland), Amsterdam EN properly colored cycles properly colored paths edge-colored graphs

doi:10.1016/j.dam.2011.06.005

Summary: In an edge-colored graph, let $d^{c}(v)$ be the number of colors on the edges incident to $v$ and let $\delta ^{c}(G)$ be the minimum $d^{c}(v)$ over all vertices $v\in G$. In this work, we consider sharp conditions on $\delta ^{c}(G)$ which imply the existence of properly edge-colored paths and cycles, meaning no two consecutive edges have the same color.