Name
Abstract | ||
|---|---|---|
We prove that the genus polynomials of the graphs called iterated claws are real-rooted. This continues our work directed toward the 25-year-old conjecture that the genus distribution of every graph is log-concave. We have previously established log-concavity for sequences of graphs constructed by iterative vertex-amalgamation or iterative edge-amalgamation of graphs that satisfy a commonly observable condition on their partitioned genus distributions, even though it had been proved previously that iterative amalgamation does not always preserve real-rootedness of the genus polynomial of the iterated graph. In this paper, the iterated topological operation is adding a claw, rather than vertex- or edge-amalgamation. Our analysis here illustrates some advantages of employing a matrix representation of the transposition of a set of productions. |
Year | Venue | Keywords |
|---|---|---|
2016 | ARS MATHEMATICA CONTEMPORANEA | Topological graph theory,graph genus polynomials,log-concavity,real-rootedness |
Field | DocType | Volume |
Topology,Discrete mathematics,Combinatorics,Line graph,Graph property,Genus (mathematics),Pathwidth,Topological graph theory,1-planar graph,Planar graph,Mathematics,Graph coloring | Journal | 10 |
Issue | ISSN | Citations |
2 | 1855-3966 | 0 |
PageRank | References | Authors |
0.34 | 7 | 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 |