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All Journal Electronic Journal of Graph Theory and Applications (EJGTA) JTAM (Jurnal Teori dan Aplikasi Matematika) Milang Journal of Mathematics and Its Applications
Fendy Septyanto
IPB University
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Electrical & Electronics Engineering Mathematics

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Journal : Electronic Journal of Graph Theory and Applications (EJGTA)

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Color code techniques in rainbow connection Fendy Septyanto; Kiki A. Sugeng
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (2018): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2018.6.2.14

Abstract

Let G be a graph with an edge k-coloring γ : E(G) → {1, …, k} (not necessarily proper). A path is called a rainbow path if all of its edges have different colors. The map γ is called a rainbow coloring if any two vertices can be connected by a rainbow path. The map γ is called a strong rainbow coloring if any two vertices can be connected by a rainbow geodesic. The smallest k for which there is a rainbow k-coloring (resp. strong rainbow k-coloring) on G is called the rainbow connection number (resp. strong rainbow connection number) of G, denoted rc(G) (resp. src(G)). In this paper we generalize the notion of “color codes” that was originally used by Chartrand et al. in their study of the rc and src of complete bipartite graphs, so that it now applies to any connected graph. Using color codes, we prove a new class of lower bounds depending on the existence of sets with common neighbours. Tight examples are discussed, involving the amalgamation of complete graphs, generalized wheel graphs, and a special class of sequential join of graphs.
Co-Authors Berlian Setiawaty D. S. Rahmawati I Gusti Putu Purnaba I Gusti Putu Purnaba I Gusti Putu Purnaba Indrya Adilla Kiki A. Sugeng Kumala Intansari Retno Budiarti Retno Budiarti Ruhiyat Ruhiyat Windiani Erliana Windiani Erliana Yuda Ardiansyah