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| Paper IPM / M / 18479 |
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| Abstract: | |
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Over half a century ago, Erd\H{o}s, Hajnal, and Rado introduced a variant of the classic problem of determining the Ramsey number for a given graph. This variant poses the following question: For a graph $ G $ and an integer $ t \geq 2 $, what is the smallest number $ N $ such that any $ t $-colored complete graph with $ N $ vertices contains a monochromatic copy of $ G $ using only $ t-1 $ colors.
In this paper, we explore these numbers specifically for linear forests, providing new insights and results.
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