On the Expression of Graph Properties in some Fragments of Monadic Second-Order Logic

: We review the expressibility of some basic graph properties in certain fragments of Monadic Second-Order logic, like the set of Monadic-NP formulas. We focus on cases where a property and its negation are both expressible in the same (or in closely related) fragments. We examine cases where edge quantifications can be eliminated and cases where they cannot. We compare two logical expressions of planarity: one of them is constructive in the sense that it defines a planar embedding of the considered graph if it is planar and 3-connected, and the other, logically simpler, uses the forbidden Kuratowski subgraphs.

• Type: Conference
• Year: 1996
• Where: DIMACS
• Authors: Bruno Courcelle
• Keywords: Basic Graph Properties, Certain Fragments, DIMACS 1996, DIMACS 2001, Monadic Second-order Logic