Name
Abstract | ||
|---|---|---|
Grunbaum and Malkevitch proved that the shortness coefficient of cyclically 4- edge-connected cubic planar graphs is at most 76/77. Recently, this was improved to 359/366 (< 52/53) and the question was raised whether this can be strengthened to 41/42, a natural bound inferred from one of the Faulkner-Younger graphs. We prove that the shortness coefficient of cyclically 4-edge-connected cubic planar graphs is at most 37/38 and that we also get the same value for cyclically 4-edge-connected cubic graphs of genus g for any prescribed genus g >= 0. We also show that 45/46 is an upper bound for the shortness coefficient of cyclically 4-edge-connected cubic graphs of genus g with face lengths bounded above by some constant larger than 22 for any prescribed g >= 0. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.37236/8440 | ELECTRONIC JOURNAL OF COMBINATORICS |
Field | DocType | Volume |
Discrete mathematics,Combinatorics,Cubic graph,Mathematics | Journal | 27 |
Issue | ISSN | Citations |
1 | 1077-8926 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| On-Hei Solomon Lo | 1 | 0 | 2.03 |
| Jens M. Schmidt | 2 | 0 | 0.34 |
| Nico Van Cleemput | 3 | 16 | 6.31 |
| Carol T. Zamfirescu | 4 | 38 | 15.25 |