A357358 Length of the longest induced cycle in the n X n torus grid graph.

6, 8, 15, 20, 28, 40, 48, 58, 73, 88, 104, 126

Offset: 3

Author

Pontus von Brömssen, Sep 25 2022

Keywords

• nonn
• more

Comments

It is somewhat unclear how a(2) should be defined. If the 2 X 2 torus grid graph is considered to have multiple edges we have a(2) = 2 (a double edge between two nodes makes a 2-cycle), otherwise a(2) = 4.

Examples

			Longest induced cycles for 3 <= n <= 8:
  X . X   X . . X   X . X . X   X X X . . .   X . X . X . X   X . X . X X . X
  X X .   X X . .   X . X X .   X . X X X .   X . X . X X .   X . X X . X X .
  . X X   . X X .   X X . X .   X X . . X .   X . X X . X .   X X . X X . X .
          . . X X   . X . X X   . X . . X X   X X . X . X .   . X X . X . X X
                    . X X . X   . X X X . X   . X . X . X X   X . X . X X . X
                                . . . X X X   . X . X X . X   X . X X . X X .
                                              . X X . X . X   X X . X X . X .
                                                              . X X . X . X X
		

Links

• Wikipedia, Induced path.

Crossrefs

Cf. A000937, A297669, A357357, A357359.

Formula

a(n) ~ 2*n^2/3.

a(n) <= A357359(n) + 1.

Extensions

a(9)-a(12) from Elijah Beregovsky, Dec 11 2022

a(13)-a(14) from Elijah Beregovsky, Dec 13 2022