Graphs with large (1,2)-rainbow connection numbers

Trung Duy Doan, Thi Thanh Chau Do and Ingo Schiermeyer

Applied Mathematics and Computation, 2024, vol. 479, issue C

Abstract: Let G be an edge-colored graph. If every subpath of length at most l+1 within a path P in a graph G consists of uniquely colored edges, then P is called an l-rainbow path. A connected graph G is deemed (1,2)-rainbow connected if there exists at least one 2-rainbow path connecting two distinct vertices within G. The minimum number of colors needed to attain (1,2)-rainbow connectedness in a connected graph G, represented as rc1,2(G), is referred to as the (1,2)-rainbow connection number. If G is a nontrivial connected graph of size m, then rc1,2(G)=m if and only if G is the star or double star of size m. Our main goal is to identify all connected graphs G of size m that satisfy the condition m−3≤rc1,2(G)≤m−1.

Keywords: Edge-coloring; Rainbow connection number; Generalized rainbow connection number; (1,2)-rainbow connection (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003473

DOI: 10.1016/j.amc.2024.128886

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