A245230 Triangle T(m,n), 1<=n<=m, read by rows: maximum frustration of complete bipartite graph K(m,n).

0, 0, 1, 0, 1, 2, 0, 2, 3, 4, 0, 2, 3, 5, 7, 0, 3, 4, 7, 9, 11, 0, 3, 5, 8, 10, 13, 16, 0, 4, 6, 10, 12, 16, 19, 22

Offset

1,6

Comments

The maximum frustration of a graph is the maximum cardinality of a set of edges that contains at most half the edges of any cut-set. Another term that is used is "line index of imbalance". It is also equal to the covering radius of the coset code of the graph.

T(m,n) is symmetric in m and n, so only m>=n is listed here.

T(m,1) = 0.

T(m,2) = floor(m/2) = A004526(m).

T(m,3) = floor(3*m/4) = A057353(m).

T(m,4) = A245231(m).

T(m,5) = A245227(m).

T(m,6) = A245239(m).

T(m,7) = A245314(m).

Links

Table of n, a(n) for n=1..36.

G. S. Bowlin, Maximum Frustration in Bipartite Signed Graphs, Electr. J. Comb. 19(4) (2012) #P10.

R. L. Graham and N. J. A. Sloane, On the Covering Radius of Codes, IEEE Trans. Inform. Theory, IT-31(1985), 263-290

P. Solé and T. Zaslavsky, A Coding Approach to Signed Graphs, SIAM J. Discr. Math 7 (1994), 544-553

Example

For m=n=3 a set of edges attaining the maximum cardinality T(3,3)=2 is {(1,4),(2,5)}.
Triangle starts
  0;
  0, 1;
  0, 1, 2;
  0, 2, 3, 4;
  0, 2, 3, 5, 7;
  0, 3, 4, 7, 9,  11;
  0, 3, 5, 8, 10, 13, 16;
  0, 4, 6, 10, 12, 16, 19, 22.

Crossrefs

Cf. A245231 (row/column 4), A245227 (row/column 5), A245239 (row/column 6), A245314 (row/column 7)

Sequence in context: A335335 A261217 A352957 * A284268 A063180 A263624

Adjacent sequences: A245227 A245228 A245229 * A245231 A245232 A245233

Keyword

nonn,tabl

Author

Robert Israel, Jul 14 2014

Status

approved