Name
Abstract | ||
|---|---|---|
The local chromatic number is a coloring parameter defined as the minimum number of colors that should appear in the most colorful closed neighborhood of a vertex under any proper coloring of the graph. Its directed version is the same when we consider only outneighborhoods in a directed graph. For digraphs with all arcs being present in both directions the two values are obviously equal. Here, we consider oriented graphs. We show the existence of a graph where the directed local chromatic number of all oriented versions of the graph is strictly less than the local chromatic number of the underlying undirected graph. We show that for fractional versions the analogous problem has a different answer: there always exists an orientation for which the directed and undirected values coincide. We also determine the supremum of the possible ratios of these fractional parameters, which turns out to be e, the basis of the natural logarithm. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1002/jgt.21834 | Journal of Graph Theory |
Keywords | Field | DocType |
local chromatic number,oriented graphs,fractional colorings | Discrete mathematics,Topology,Edge coloring,Combinatorics,Fractional coloring,Directed graph,Null graph,Friendship graph,Butterfly graph,Windmill graph,Mathematics,Critical graph | Journal |
Volume | Issue | ISSN |
79 | 4 | 0364-9024 |
Citations | PageRank | References |
1 | 0.35 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gábor Simonyi | 1 | 249 | 29.78 |
| Gábor Tardos | 2 | 1261 | 140.58 |
| Ambrus Zsbán | 3 | 12 | 1.98 |