Stefan Szeider

Herbert Fleischner; Oliver Kullmann; Stefan Szeider

A formula (in conjunctive normal form) is said to be minimal unsatisfiable if it is unsatisfiable and deleting any clause makes it satisfiable. The deficiency of a formula is the difference of the number of clauses and the number of variables. It is known that every minimal unsatisfiable formula has positive deficiency. Until recently, polynomial-time algorithms were known to recognize minimal unsatisfiable formulas with deficiency 1 and 2. We state an algorithm which recognizes minimal unsatisfiable formulas with any fixed deficiency in polynomial time.

Michael R. Fellows; Frances A. Rosamond; Udi Rotics; Stefan Szeider

Clique-width is a graph parameter that measures in a certain sense the complexity of a graph. Hard graph problems (e.g., problems expressible in monadic second-order logic with second-order quantification on vertex sets, which includes NP-hard problems such as 3-colorability) can be solved in polynomial time for graphs of bounded clique-width. We show that the clique-width of a given graph cannot be absolutely approximated in polynomial time unless

Marko Samer; Stefan Szeider

P = NP

Stefan Szeider

. We also show that, given a graph

Georg Gottlob; Stefan Szeider

G

Marko Samer; Stefan Szeider

and an integer

Marko Samer; Stefan Szeider

k

Serge Gaspers; Stefan Szeider

, deciding whether the clique-width of

Sanjay Modgil; Francesca Toni; Floris Bex; Ivan Bratko; Carlos Iván Chesñevar; Wolfgang Dvořák; Marcelo Alejandro Falappa; Xiuyi Fan; Sarah Alice Gaggl; Alejandro Javier García; María Paula González; Thomas F. Gordon; João Leite; Martin Možina; Chris Reed; Guillermo Ricardo Simari; Stefan Szeider; Paolo Torroni; Stefan Woltran

G

Luke Mathieson; Stefan Szeider

is at most