A very large part of combinatorics deals or can be formulated as to deal with optimization problems in discrete structures. Generally, the constraints and the objective function are linear forms of certain variables that are restricted to integers or, mostly, to 0 and 1. Thus, the combinatorial problem is translated to a linear integer-programming problem. The value of such a translation depends on whether it provides new insight or new methods for the solution. This chapter discusses several most important results in integer programming that have been successfully applied to graph theory and then discusses those fields of graph theory where an integer-programming approach has been most effective. The chapter also discusses many graph theoretical results that have a linear programming flavor but no explicit treatment.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics