The class reconstruction number of maximal planar graphs
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The reconstruction numberrn(G) of a graphG was introduced by Harary and Plantholt as the smallest number of vertex-deleted subgraphsG i =G − v i in the deck ofG which do not all appear in the deck of any other graph. For any graph theoretic propertyP, Harary defined theP-reconstruction number of a graph G ∈P as the smallest number of theG i in the deck ofG, which do not all appear in the deck of any other graph inP We now study the maximal planar graph reconstruction numberℳrn(G), proving that its value is either 1 or 2 and characterizing those with value 1.
KeywordsPlanar Graph Graph Reconstruction Maximal Planar Graph Class Reconstruction Reconstruction Number
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