cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A245762 Maximal number of edges in a C_4 free subgraph of the n-cube.

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%I A245762 #28 Sep 01 2025 11:23:44
%S A245762 1,3,9,24,56,132
%N A245762 Maximal number of edges in a C_4 free subgraph of the n-cube.
%C A245762 This is related to the famous conjecture of Erdős (see Erdős link).
%D A245762 M. R. Emamy, K. P. Guan and I. J. Dejter, On fault tolerance in a 5-cube. Preprint.
%D A245762 H. Harborth and H. Nienborg, Maximum number of edges in a six-cube without four-cycles, Bulletin of the ICA 12 (1994) 55-60
%H A245762 Thomas Bloom, <a href="http://www.math.ucsd.edu/~erdosproblems/erdos/newproblems/TuranInCube.html">Subgraphs of the cube without a 2k-cycle</a>, Erdős Problems.
%H A245762 P. Brass, H. Harborth and H. Nienborg, <a href="http://dx.doi.org/10.1002/jgt.3190190104">On the maximum number of edges in a c4-free subgraph of qn</a>, J. Graph Theory 19 (1995) 17-23
%H A245762 F. R. K. Chung, <a href="http://dx.doi.org/10.1002/jgt.3190160311">Subgraphs of a hypercube containing no small even cycles</a>, J. Graph Theory 16 (1992) 273-286
%H A245762 Manfred Scheucher and Paul Tabatabai, <a href="/A245762/a245762.py.txt">Python Script</a>
%e A245762 a(2) = 3 since the 2-cube is the 4-cycle and one needs to remove a single edge to get rid of all 4-cycles.
%K A245762 nonn,more,changed
%O A245762 1,2
%A A245762 _Jernej Azarija_, Jul 31 2014
%E A245762 a(6) from _Manfred Scheucher_ and _Paul Tabatabai_, Jul 23 2015