The 40th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2014) was held in Nouan-le-Fuzelier near Orléans, France on June 25–27. The WG 2014 Program Committee selected 32 high-quality papers among 80 submissions, for presentation at the conference and publication in the conference proceedings. Three of those papers, among the best ones, were proposed by the PC of WG 2014 for possible publication as selected papers in Algorithmica. It turns out that the subjects of the selected papers nicely illustrate some of the main, classical topics of WG conferences: structure of graph classes, graph algorithms and width parameters. The three papers went through a standard refereeing process of Algorithmica before being accepted for publication in this issue:

  • Boxicity and Separation Dimension by Manu Basavaraju, L. Sunil Chandran, Martin Charles Golumbic, Rogers Mathew and Deepak Rajendraprasad

  • A new characterization of \(P_k\)-free graphs by Eglantine Camby and Oliver Schaudt

  • Between Treewidth and Clique-Width by Sigve Hortemo Sæther and Jan Arne Telle.

We wish to thank the referees for their careful and thorough reviewing and their comments which helped the authors improving their papers.