Let rex(n,F) denote the maximum number of edges in an n-vertex graph that is regular and does not contain F as a subgraph. We give lower bounds on rex(n,F), are best possible up to constant factor, when one C4, K2,t, K3,3 or Ks,t for t>s!.

If G is a graph and H set of subgraphs , we say that an edge-coloring -polychromatic if every from gets all colors present in on its edges. The number denoted by poly ( ) the largest coloring. In this paper determine exactly when complete n vertices, q fixed nonnegative integer, one three families: family matchings spanning − 2-regular graphs at least cycles length precisely . There are connect...

We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language – the input of the problem – and fixed language called filter is non-empty. We consider two kind of problems depending on representation of regular language. If a regular language on input is represented by a DFA, then we obtain (deterministic) regular realizability...

We investigate the complexity of deciding whether a given regular language can be defined with a deterministic regular expression. Our main technical result shows that the problem is PSPACE-complete if the input language is represented as a regular expression or nondeterministic finite automaton. The problem becomes EXPSPACE-complete if the language is represented as a regular expression with c...

Membership problems for compressed strings in regular languages are investigated. Strings are represented by straight-line programs, i.e. contextfree grammars that generate exactly one string. For the representation of regular languages, various formalisms with different degrees of succinctness (e.g. suitably extended regular expressions, hierarchical automata) are considered. Precise complexit...

Membership problems for compressed strings in regular languages are investigated. Strings are represented by straight-line programs, i.e., context-free grammars that generate exactly one string. For the representation of regular languages, various formalisms with different degrees of succinctness (e.g., suitably extended regular expressions, hierarchical automata) are considered. Precise comple...