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Given a graph G and a positive integer k , define the Gallai-Ramsey number to be the minimum number of vertices n such that any k -edge coloring of $$K_n$$… Click to show full abstract
Given a graph G and a positive integer k , define the Gallai-Ramsey number to be the minimum number of vertices n such that any k -edge coloring of $$K_n$$ K n contains either a rainbow (all different colored) triangle or a monochromatic copy of G . In this paper, we consider two classes of unicyclic graphs, the star with an extra edge and the path with a triangle at one end. We provide the 2-color Ramsey numbers for these two classes of graphs and use these to obtain general upper and lower bounds on the Gallai-Ramsey numbers.
Keywords:
classes unicyclic;
unicyclic graphs;
two classes;
ramsey;
ramsey numbers;
gallai ramsey
Journal Title: Graphs and Combinatorics
Year Published: 2021
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Journal Title: Graphs and Combinatorics
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!