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

Author

Listed:
  • Doan, Trung Duy
  • Do, Thi Thanh Chau
  • Schiermeyer, Ingo

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.

Suggested Citation

  • Doan, Trung Duy & Do, Thi Thanh Chau & Schiermeyer, Ingo, 2024. "Graphs with large (1,2)-rainbow connection numbers," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    • Handle: RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003473
    DOI: 10.1016/j.amc.2024.128886
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