Name
Abstract | ||
|---|---|---|
A face of a vertex coloured plane graph is called loose if the number of colours used on its vertices is at least three. The looseness of a plane graph G is the minimum k such that any surjective k-colouring involves a loose face. In this paper we prove that the looseness of a connected plane graph G equals the maximum number of vertex disjoint cycles in the dual graph G* increased by 2. We also show upper bounds on the looseness of graphs based on the number of vertices, the edge connectivity, and the girth of the dual graphs. These bounds improve the result of Negami for the looseness of plane triangulations. We also present infinite classes of graphs where the equalities are attained. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/s00373-010-0961-6 | Graphs and Combinatorics |
Keywords | Field | DocType |
dual graph,plane triangulations,vertex disjoint cycle,minimum k,plane graph g,vertex colouring · loose colouring · looseness · plane graph · dual graph,connected plane graph,plane graphs,vertex coloured plane graph,maximum number,edge connectivity,loose face,plane graph,upper bound | Topology,Discrete mathematics,Combinatorics,Vertex (graph theory),Neighbourhood (graph theory),Cycle graph,Dual graph,Symmetric graph,Pathwidth,1-planar graph,Planar graph,Mathematics | Journal |
Volume | Issue | ISSN |
27 | 1 | 1435-5914 |
Citations | PageRank | References |
1 | 0.35 | 10 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Július Czap | 1 | 80 | 15.40 |
| Stanislav Jendrol’ | 2 | 67 | 7.66 |
| František Kardoš | 3 | 87 | 9.72 |
| Jozef Miškuf | 4 | 51 | 5.20 |