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 f0 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 f0 connected components of set S \ J. We say that route C = v1 e1 v2 e2 ... vk in a flat graph G has ordered enclosing if for any its initial part C1 = v1 e1 v2 e2 ... el, l ≤ | E | the condition Int (Cl) ∩ 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 | ṡ log2 | V |). © 2007 Elsevier B.V. All rights reserved.