
Asymptotically Optimal Vertex Ranking of Planar Graphs
A (vertex) ℓranking is a labelling φ:V(G)→ℕ of the vertices of a graph ...
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Optimal labelling schemes for adjacency, comparability and reachability
We construct asymptotically optimal adjacency labelling schemes for ever...
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Parallel Planar Subgraph Isomorphism and Vertex Connectivity
We present the first parallel fixedparameter algorithm for subgraph iso...
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Local certification of graphs on surfaces
A proof labelling scheme for a graph class 𝒞 is an assignment of certifi...
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Multilayered planar firefighting
Consider a model of fire spreading through a graph; initially some verti...
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Adjacency Graphs of Polyhedral Surfaces
We study whether a given graph can be realized as an adjacency graph of ...
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Graphs without gapvertexlabellings: families and bounds
A proper labelling of a graph G is a pair (π,c_π) in which π is an assig...
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Adjacency Labelling for Planar Graphs (and Beyond)
We show that there exists an adjacency labelling scheme for planar graphs where each vertex of an nvertex planar graph G is assigned a (1+o(1))log_2 nbit label and the labels of two vertices u and v are sufficient to determine if uv is an edge of G. This is optimal up to the lower order term and is the first such asymptotically optimal result. An alternative, but equivalent, interpretation of this result is that, for every n, there exists a graph U_n with n^1+o(1) vertices such that every nvertex planar graph is an induced subgraph of U_n. These results generalize to bounded genus graphs, apexminorfree graphs, boundeddegree graphs from minor closed families, and kplanar graphs.
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