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- W4300772539 abstract "The rainbow connection number, $rc(G)$, of a connected graph $G$ is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same. We show that for $kappa =3$ or $kappa = 4$, every $kappa$-connected graph $G$ on $n$ vertices with diameter $frac{n}{kappa}-c$ satisfies $rc(G) leq frac{n}{kappa} + 15c + 18$. We also show that for every maximal planar graph $G$, $rc(G) leq frac{n}{kappa} + 36$. This proves a conjecture of Li et al. for graphs with large diameter and maximal planar graphs." @default.
- W4300772539 created "2022-10-04" @default.
- W4300772539 creator A5034695977 @default.
- W4300772539 date "2012-12-24" @default.
- W4300772539 modified "2023-09-27" @default.
- W4300772539 title "Some Bounds on the Rainbow Connection Number of 3-, 4- and 5-connected Graphs" @default.
- W4300772539 doi "https://doi.org/10.48550/arxiv.1212.5934" @default.
- W4300772539 hasPublicationYear "2012" @default.
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