Proper vertex-pancyclicity of edge-colored complete graphs without monochromatic triangles

In an edge-colored graph (G, c), let d(c)(v) be the number of colors on the edges incident to vertex v and let delta(c)(G) be the minimum value of d(c)(v) over all vertices v is an element of V(G). A cycle of (G, c) is called proper if any two adjacent edges of the cycle have distinct colors. An edge-colored graph (G, c) on n >= 3 vertices is called properly vertex-pancyclic if each vertex of (G, c) is contained in a proper cycle of length I for every I with 3 <= l <= n. Fujita and Magnant conjectured that every edge-colored complete graph on n >= 3 vertices with delta(c)(G) >= n+1/2 is properly vertex-pancyclic. We show that this conjecture is true if the edge-colored complete graph has no monochromatic triangles. (C) 2019 Elsevier B.V. All rights reserved.