Name
Abstract | ||
|---|---|---|
The 25-year old LCGD Conjecture is that the genus distribution of every graph is log-concave. We present herein a new topological conjecture, called the Local Log-Concavity Conjecture. We also present a purely combinatorial conjecture, which we prove to be equivalent to the Local Log-Concavity Conjecture. We use the equivalence to prove the Local Log-Concavity Conjecture for graphs of maximum degree four. We then show how a formula of David Jackson could be used to prove log-concavity for the genus distributions of various partial rotation systems, with straight-forward application to proving the local log-concavity of additional classes of graphs. We close with an additional conjecture, whose proof, along with proof of the Local Log-Concavity Conjecture, would affirm the LCGD Conjecture. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.ejc.2015.10.002 | European Journal of Combinatorics |
Field | DocType | Volume |
Reconstruction conjecture,Discrete mathematics,Combinatorics,abc conjecture,Prime gap,Elliott–Halberstam conjecture,Lonely runner conjecture,Goldbach's weak conjecture,Collatz conjecture,Mathematics,Erdős–Gyárfás conjecture | Journal | 52 |
Issue | ISSN | Citations |
PA | 0195-6698 | 0 |
PageRank | References | Authors |
0.34 | 4 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jonathan L. Gross | 1 | 458 | 268.73 |
| Toufik Mansour | 2 | 423 | 87.76 |
| Thomas W. Tucker | 3 | 191 | 130.07 |
| David G. L. Wang | 4 | 18 | 6.52 |