Mathematical Sciences: Faculty Publications
Forbidden Properly Edge-Colored Subgraphs that Force Large Highly Connected Monochromatic Subgraphs
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 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.
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
Copyright
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