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On some interconnections between combinatorial optimization and extremal graph theory

Cvetković Dragoš M. (Faculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia and Montenegro)
Hansen Pierre (GERAD and École des Hautes Études Commerciales, Montréal HT A, Canada)
Kovačević-Vujčić Vera V. (Faculty of Organizational Sciences, University of Belgrade, Belgrade, Serbia and Montenegro)

The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants under some constraints and with constructing extremal graphs. We analyze by examples some interconnections and interactions of the two theories and propose some conclusions.

Keywords: combinatorial optimization, extremal graph theory, variable neighborhood search, mathematical programming.