Local Finiteness, Distinguishing Numbers, and Tucker's Conjecture
Copyright policy )Local Finiteness, Distinguishing Numbers, and Tucker's Conjecture
A distinguishing colouring of a graph is a colouring of the vertex set such that no non-trivial automorphism preserves the colouring. Tucker conjectured that if every non-trivial automorphism of a locally finite graph moves infinitely many vertices, then there is a distinguishing 2-colouring. We show that the requirement of local finiteness is necessary by giving a non-locally finite graph for which no finite number of colours suffices.
- University of Iceland Iceland
- Universität Hamburg Germany
infinite graphs, Coloring of graphs and hypergraphs, Infinite graphs, Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05C25 (Primary), 05C63, 05C15 (Secondary), distinguishing number, Graphs and abstract algebra (groups, rings, fields, etc.)
infinite graphs, Coloring of graphs and hypergraphs, Infinite graphs, Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05C25 (Primary), 05C63, 05C15 (Secondary), distinguishing number, Graphs and abstract algebra (groups, rings, fields, etc.)
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