Forbidden Properly Edge-Colored Subgraphs that Force Large Highly Connected Monochromatic Subgraphs
Graphs and Combinatorics
We consider the connected graphs G that satisfy the following property: If n≫m≫k are integers, then any coloring of the edges of Kn, using m colors, containing no properly colored copy of G, contains a monochromatic k-connected subgraph of order at least n−f(G,k,m) where f does not depend on n. If we let G denote the set of graphs satisfying this statement, we exhibit some infinite families of graphs in G as well as conjecture that the cycles in G are precisely those whose lengths are divisible by 3. Our main result is that C6∈G.
Katic, Robert, Colton Magnant, Pouria Salehi Nowbandegani.
"Forbidden Properly Edge-Colored Subgraphs that Force Large Highly Connected Monochromatic Subgraphs."
Graphs and Combinatorics, 33 (4): 969-979.