Forbidden Properly Edge-Colored Subgraphs that Force Large Highly Connected Monochromatic Subgraphs

Authors

Robert Katic, Georgia Southern UniversityFollow
Colton Magnant, Georgia Southern UniversityFollow
Pouria Salehi Nowbandegani, Vanderbilt UniversityFollow

Document Type

Article

Publication Date

7-2017

Publication Title

Graphs and Combinatorics

DOI

10.1007/s00373-017-1804-5

ISSN

1435-5914

Abstract

We consider the connected graphs G that satisfy the following property: If n≫m≫k are integers, then any coloring of the edges of K_n, 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.

Recommended Citation

Katic, Robert, Colton Magnant, Pouria Salehi Nowbandegani. 2017. "Forbidden Properly Edge-Colored Subgraphs that Force Large Highly Connected Monochromatic Subgraphs." Graphs and Combinatorics, 33 (4): 969-979. doi: 10.1007/s00373-017-1804-5
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/592