Groupe d’études et de recherche en analyse des décisions

G-92-38

The Clar Number of a Benzenoid Hydrocarbon and Linear Programming

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It is shown that the Clar number of a benzenoid hydrocarbon H (defined as the number of circles in a Clar formula, or equivalently as the maximum number of mutually resonant hexagons of H) can be determined by mixed-integer programming. Moreover, linear programming appears to suffice in practice to find in moderate computing time the Clar number of pericondensed hydrocarbons with more than a thousand hexagons.

, 21 pages