On $(t-1)$-colored paths in $t$-colored complete graphs

The (t−1) $(t-1)$‐chromatic Ramsey number for paths

“…First to explicitly ask the question of determining the $$(t-1)$$‐chromatic Ramsey number for noncomplete graphs were Chung and Liu in 1978. This question has been considered for a number of families of graphs over the years [3, 8–10, 16, 17, 20, 23–28]. In this paper we are interested in the $$(t-1)$$‐chromatic Ramsey number of a path.…”

“…Since the case of $$t=2$$ corresponds to the classical 2‐colour Ramsey problem, it is solved completely by the result of Gerencsér and Gyárfás [15]. For $$3\le t\le 5$$ the value of $${R}_{t-1}^{t}({P}_{\ell })$$ was determined in [25, 26, 32]. In this paper we determine the answer precisely for any number of colours, answering a question raised in [26].…”

A note on (t - 1)-chromatic Ramsey number of linear forests

“…The exact value of the (t − 1)-chromatic Ramsey number of paths when the number of colors is three, four or five is known. 11]).…”