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core (907B)


      1 # Core
      2 
      3 The [core] of an [instance] A is a [subinstance] B of A such that there is no [homomorphism] from B to a strict [subinstance] B' of B
      4 - this is unique up to [isomorphism]
      5 - it is equal to A if there is no [endomorphism] from A to a strict [subinstance] of A
      6 
      7 [computational_problem] of computing the core:
      8 - checking if a [graph] is its own core
      9   - clearly in [coNP] (guess the [homomorphism])
     10   - [conp_complete]
     11     - https://cstheory.stackexchange.com/questions/2733/what-is-the-best-exact-algorithm-to-compute-the-core-of-a-graph
     12 - checking if input [graph] G is core of input [graph] H
     13   - is in [dp]:
     14     - guess existence of [homomorphism]
     15     - guess inexistence of other [homomorphism]
     16   - is [dp_complete] by [fagin2005data2]
     17   - https://cstheory.stackexchange.com/questions/2733/what-is-the-best-exact-algorithm-to-compute-the-core-of-a-graph
     18 
     19 Up: [homomorphism]
     20 
     21 See also: [chase_core]