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Elusive extremal graphs
- Publication Year :
- 2018
-
Abstract
- We study the uniqueness of optimal solutions to extremal graph theory problems. Lovasz conjectured that every finite feasible set of subgraph density constraints can be extended further by a finite set of density constraints so that the resulting set is satisfied by an asymptotically unique graph. This statement is often referred to as saying that `every extremal graph theory problem has a finitely forcible optimum'. We present a counterexample to the conjecture. Our techniques also extend to a more general setting involving other types of constraints.
- Subjects :
- Mathematics - Combinatorics
Computer Science - Discrete Mathematics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1807.01141
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1112/plms.12382