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• W2093753205 abstract "In the wake of the resolution of the four-color conjecture, the graph reconstruction conjecture has emerged as one focal point of graph theory. This paper considers thecomputational complexity of decision problems (Deck Checking andLegitimate Deck), construction problems (Preimage Construction), and counting problems (Preimage Counting) related to the graph reconstruction conjecture. We show that: 1. $${text{GRAPH}} {text{ISOMORPHISM}} leqslant _m^l LEGITIMATE DECK, and$$ 2 $${text{GRAPH}} {text{ISOMORPHISM}} equiv _{iso}^l DECK CHECKING.$$ Relatedly, we display the first natural GI-hard NP set lacking obvious padding functions. Finally, we show thatLegitimate Deck, Preimage Construction, andPreimage Counting are solvable in polynomial time for graphs of bounded degree, partialk-trees for any fixedk, and graphs of bounded genus, in particular for planar graphs." @default.
• W2093753205 created "2016-06-24" @default.
• W2093753205 creator A5029412954 @default.
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• W2093753205 date "1994-05-01" @default.
• W2093753205 modified "2023-10-11" @default.
• W2093753205 title "On the complexity of graph reconstruction" @default.
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• W2093753205 doi "https://doi.org/10.1007/bf01578845" @default.
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