Eulerian Cover with Ordered Enclosing for Flat Graphs

Abstract Let S be a plane, let G = ( V , E ) be a flat graph on S, and let f 0 be exterior (infinite) face of graph G. Let's consider partial graph J ⊂ G . Through lnt ( J ) we shall designate the subset of S which is union of all not containing exterior face f 0 connected components of set S \ J . We say that route C = v 1 e 1 v 2 e 2 … v k in a flat graph G has ordered enclosing if for any its initial part C 1 = v 1 e 1 v 2 e 2 … e l , l ⩽ | E | the condition Int ( C l ) ∩ E = ∅ is hold. The paper presents the algorithm constructing the cover of flat connected graph without end-vertexes by the minimal cardinality sequence of chains with ordered enclosing. The correctness of the constructed algorithm is proved. Computing complexity of the algorithm O ( | E | ⋅ log 2 | V | ) .