Name
Abstract | ||
|---|---|---|
The vertex-edge marking game is played between two players on a graph, $G=(V,E)$, with one player marking vertices and the other marking edges. The players want to minimize/maximize, respectively, the number of marked edges incident to an unmarked vertex. The vertex-edge coloring number for $G$ is the maximum score achievable with perfect play. Bre\v{s}ar et al., [4], give an upper bound of $5$ for the vertex-edge coloring number for finite planar graphs. It is not known whether the bound is tight. In this paper, in response to questions in [4], we show that the vertex-edge coloring number for the infinite regular triangularization of the plane is 4. We also give two general techniques that allow us to calculate the vertex-edge coloring number in many related triangularizations of the plane. |
Year | Venue | DocType |
|---|---|---|
2022 | Australasian Journal of Combinatorics | Journal |
Volume | ISSN | Citations |
84 | 1034-4942 | 0 |
PageRank | References | Authors |
0.34 | 0 | 11 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daniel Herden | 1 | 0 | 0.34 |
| Jonathan Meddaugh | 2 | 0 | 0.34 |
| Mark Sepanski | 3 | 0 | 0.34 |
| Isaac Echols | 4 | 0 | 0.34 |
| Nina Garcia-Montoya | 5 | 0 | 0.34 |
| Cordell Hammon | 6 | 0 | 0.34 |
| Guanjie Huang | 7 | 0 | 1.01 |
| Adam Kraus | 8 | 0 | 0.34 |
| Jorge Marchena Menendez | 9 | 0 | 0.34 |
| Jasmin Mohn | 10 | 0 | 0.34 |
| Rafael Morales Jiménez | 11 | 0 | 0.34 |