
Adjacency Labelling for Planar Graphs (and Beyond)
We show that there exists an adjacency labelling scheme for planar graph...
read it

Smaller extended formulations for spanning tree polytopes in minorclosed classes and beyond
Let G be a connected nvertex graph in a proper minorclosed class π’. We...
read it

Optimal labelling schemes for adjacency, comparability and reachability
We construct asymptotically optimal adjacency labelling schemes for ever...
read it

The Space Complexity of Sum Labelling
A graph is called a sum graph if its vertices can be labelled by distinc...
read it

Least conflict choosability
Given a multigraph, suppose that each vertex is given a local assignment...
read it

Graphs without gapvertexlabellings: families and bounds
A proper labelling of a graph G is a pair (Ο,c_Ο) in which Ο is an assig...
read it

Introduction to local certification
Local certification is an concept that has been defined and studied rece...
read it
Local certification of graphs on surfaces
A proof labelling scheme for a graph class π is an assignment of certificates to the vertices of any graph in the class π, such that upon reading its certificate and the certificate of its neighbors, every vertex from a graph Gβπ accepts the instance, while if Gβπ, for every possible assignment of certificates, at least one vertex rejects the instance. It was proved recently that for any fixed surface Ξ£, the class of graphs embeddable in Ξ£ has a proof labelling scheme in which each vertex of an nvertex graph receives a certificate of at most O(log n) bits. The proof is quite long and intricate and heavily relies on an earlier result for planar graphs. Here we give a very short proof for any surface. The main idea is to encode a rotation system locally, together with a spanning tree supporting the local computation of the genus via Euler's formula.
READ FULL TEXT
Comments
There are no comments yet.