An Update on Supereulerian Graphs
نویسندگان
چکیده
A graph is supereulerian if it has a spanning Eulerian subgraph. Motivated by the Chinese Postman Problem, Boesch, Suffel, and Tindell ([2]) in 1997 proposed the supereulerian problem, which seeks a characterization of graphs that have spanning Eulerian subgraphs, and they indicated that this problem would be very difficult. Pulleyblank ([71]) later in 1979 proved that determining whether a graph is supereulerian, even within planar graphs, is NP-complete. Since then, there have been lots of researches on this topic. Catlin ([7]) in 1992 presented the first survey on supereulerian graphs. This paper is intended as an update of Catlin’s survey article and will focus on the developments in the study of supereulerian graphs and the related problems over the past 20 years. Key–Words: Eulerian graphs, Supereulerian graphs, Collapsible graphs, Catlin’s reduction method, Line graphs, Claw-free graphs
منابع مشابه
Supereulerian graphs: A survey
A graph is supereulerian if it has a spanning eulerian subgraph. There is a reduction method to determine whether a graph is supereulerian, and it can also be applied to study other concepts, e.g., hamiltonian line graphs, a certain type of double cycle cover, and the total interval number of a graph. We outline the research on supereulerian graphs, the reduction method and its applications.
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