Name
Abstract | ||
|---|---|---|
An r-maximum k-edge-coloring of G is a k-edge-coloring of G having a property that for every vertex v of degree d(G)(v) = d, d >= r, the maximum color, that is present at vertex v, occurs at v exactly r times. The r-maximum index chi(r)' (G) is defined to be the minimum number k of colors needed for an r-maximum k-edge-coloring of graph G. In this paper we show that chi(r)' (G) <= 3 for any nontrivial connected graph G and r = 1 or 2. The bound 3 is tight. All graphs G with chi(1)' (G) = i, i = 1, 2, 3 are characterized. The precise value of the r-maximum index, r >= 1, is determined for trees and complete graphs. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.7151/dmgt.1843 | DISCUSSIONES MATHEMATICAE GRAPH THEORY |
Keywords | Field | DocType |
edge-coloring,r-maximum k-edge-coloring,unique-maximum edge-coloring,weak-odd edge-coloring,weak-even edge-coloring | Edge coloring,Graph,Complete coloring,Discrete mathematics,Combinatorics,Fractional coloring,Brooks' theorem,Mathematics | Journal |
Volume | Issue | ISSN |
36 | 1 | 1234-3099 |
Citations | PageRank | References |
1 | 0.35 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stanislav Jendrol' | 1 | 283 | 38.72 |
| Michaela Vrbjarová | 2 | 8 | 1.64 |