Variable neighborhood search for extremal graphs. 5. Three ways to automate finding conjectures

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Abstract

The AutoGraphiX system determines classes of extremal or near-extremal graphs with a variable neighborhood search heuristic. From these, conjectures may be deduced interactively. Three methods, a numerical, a geometric and an algebraic one are proposed to automate also this last step. This leads to automated deduction of previous conjectures, strengthening of a series of conjectures from Graffiti and obtention of several new conjectures, four of which are proved. © 2003 Elsevier B.V. All rights reserved.

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Caporossi, G., & Hansen, P. (2004). Variable neighborhood search for extremal graphs. 5. Three ways to automate finding conjectures. In Discrete Mathematics (Vol. 276, pp. 81–94). https://doi.org/10.1016/S0012-365X(03)00311-X

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