an:00790756
Zbl 0842.05032
Katchalski, Meir; McCuaig, William; Seager, Suzanne
Ordered colourings
EN
Discrete Math. 142, No. 1-3, 141-154 (1995).
00027770
1995
j
05C15 05C05 05C10 05C35 05C40
ordered colorings; trees; planar graphs; connectivity
An ordered \(k\)-coloring of a graph \(G\) is a coloring function \(c: V(G)\to \{1, 2,\dots, k\}\) such that, for every pair of distinct vertices \(x\) and \(y\) and for every \(x\)-\(y\) path \(P\), if \(c(x)= c(y)\), then there exists an internal vertex \(z\) of \(P\) such that \(c(x)< c(z)\). This paper proves some results about ordered colorings of trees and planar graphs. For example, if every planar graph has an ordered coloring using at least \(g(v)\) vertices, then \(g(v)\leq 3(\sqrt 6+ 2)\sqrt v\). The paper also examines the relationship between connectivity and ordered colorings.
A.Tucker (Stony Brook)