Jantzen, M., H. Petersen, Cancellation in context-free languages: enrichment by reduction, Theoretical Computer Science 127 (1994) 1499170. The following problem is shown to be decidable: Given a context-free grammar G and a string weX*, does there exist a string ueL(G) such that w is obtained from u by deleting all substrings ui that are elements of the symmetric Dyck set DT? The intersection ...

In this talk, we show an interesting fact that a quarter of paths of random walks of any length n(≥ 2) have two maximums. Moreover, it holds that the asymptotic distribution of number of maximums of paths obeys the geometric distribution of parameter 1/2. Furthermore, we provide the generating function for counting number of paths jointly with number k of maximums and number l of minimums. This...

We examine the simultaneous embedding with fixed edges problem for two planar graphs G1 and G2 with the focus on their intersection S = G1∩G2. In particular, we will present the complete set of intersection graphs S that guarantee a simultaneous embedding with fixed edges for (G1, G2). More formally, we define the subset ISEFE of all planar graphs as follows: A graph S lies in ISEFE if every pa...

We prove that the unique decomposition of connected graphs defined by Tutte is definable by formulas of Monadic Second-Order Logic. This decomposition has two levels: every connected graph is a tree of "2-connected components" called blocks ; every 2-connected graph is a tree of so-called 3-blocks. Our proof uses 2dags which are certain acyclic orientations of the considered graphs. We obtain a...

The rank-width is a graph parameter related in terms of fixed functions to cliquewidth but more tractable. Clique-width has nice algorithmic properties, but no good “minor” relation is known analogous to graph minor embedding for tree-width. In this paper, we discuss the vertex-minor relation of graphs and its connection with rank-width. We prove a relationship between vertex-minors of bipartit...

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