Forbidden families of configurations

Beyond-Planarity: Density Results for Bipartite Graphs

Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly-planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations. Early research dates back to the 1960s (e.g., Avital and Hanani [14]) for extremal problems on geometric graphs, but is also related to graph drawing problems ...

Inferring Subclasses of Regular Languages Faster Using RPNI and Forbidden Configurations

Many varieties of regular languages have characterizations in terms of forbidden-patterns of their accepting finite automata. The use of patterns while inferring languages belonging to those families through the RPNI-Lang algorithm help to avoid overgeneralization in the same way as negative samples do. The aim of this paper is to describe and prove the convergence of a modification of the RPNI...

Small Forbidden Configurations II

The present paper continues the work begun by Anstee, Griggs and Sali on small forbidden configurations. In the notation of (0,1)-matrices, we consider a (0,1)-matrix F (the forbidden configuration), an m × n (0,1)-matrix A with no repeated columns which has no submatrix which is a row and column permutation of F , and seek bounds on n in terms of m and F . We give new exact bounds for some 2× ...

No Forbidden Landscape in String/M-theory

Scale invariant but non-conformal field theories are forbidden in (1 + 1) dimension, and so should be the corresponding holographic dual gravity theories. We conjecture that such scale invariant but non-conformal field configurations do not exist in the string/M-theory. We provide a proof of this conjecture in the classical supergravity limit. Our proof does also apply in higher dimensional sca...

Linear Algebra and Forbidden Configurations