Every proper minor-closed graph class admits an optimal (1+o(1)) log n bit adjacency labeling scheme.
Sanders, Bruce Reed, Paul Seymour, and Dirk Vertigan
2 Pith papers cite this work. Polarity classification is still indexing.
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Graphs of treewidth k satisfy α_c(G) ≥ c/(c+k+1)n with matching upper-bound constructions; the bound improves to c/(c+k)n when c≤2 or k=1 and to 5/9 n when c=3 and k=2.
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Adjacency labelling for proper minor-closed graph classes
Every proper minor-closed graph class admits an optimal (1+o(1)) log n bit adjacency labeling scheme.
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Clustered independence and bounded treewidth
Graphs of treewidth k satisfy α_c(G) ≥ c/(c+k+1)n with matching upper-bound constructions; the bound improves to c/(c+k)n when c≤2 or k=1 and to 5/9 n when c=3 and k=2.