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Maximum k for which the grid graph P_3 X P_k is an induced subgraph of the n X n knight graph.
3

%I #15 Feb 15 2022 08:18:55

%S 1,1,3,4,5,6,7,10,11,12,14,16,20,21,25,28,32,34,41,44,49,53

%N Maximum k for which the grid graph P_3 X P_k is an induced subgraph of the n X n knight graph.

%H Donald E Knuth, <a href="http://cs.stanford.edu/~knuth/fasc7a.ps.gz">The Art of Computer Programming, exercises on "knight grids" in Section 7.2.2.3</a> (preliminary draft)

%H Don Knuth, <a href="http://cs.stanford.edu/~knuth/programs/back-knightgrid3-strict.w">CWEB program</a>

%e a(6) = 4 because of the following strict embedding of P3 X P4 into N6:

%e - - - - - -

%e 4 - 2 - - - where the vertices of P3 X P4 are

%e - - 4 - 2 - 1 2 3 4

%e 4 3 2 1 - - 1 2 3 4

%e - - - 3 - 1 1 2 3 4

%e - 3 - 1 - -

%Y Cf. A351389 (considers not-necessarly-induced subgraphs), A351391 (considers P2 X Pk), A351393 (considers P4 X Pk).

%K nonn,more

%O 3,3

%A _Don Knuth_, Feb 10 2022