Covering Graphs with Directed Paths

• Main Authors: Hsieh, Chi-Tsung, 謝奇璁
• Other Authors: Fu, Hung-Lin
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/98529606536829265565

碩士 === 國立交通大學 === 應用數學系所 === 97 === In this thesis we study an oriented version of perfect path double cover (PPDC). An oriented perfect path double cover (OPPDC) of a graph G is a collection of oriented paths in the symmetric orientation S(G) of G such that each edge of S(G) lies in exactly one of the paths and for each vertex v ∈ V (G) there is a unique path which begins in v (and thus the same holds also for terminal vertices of the paths). First we show that if G has no components which isomorphism to K3 and G is a 3-degenerate graph, then G has an OPPDC. Next we also construct an OPPDC for complete bipartite graph Kn,n and multipartite graph Km(n) (n is odd and m ≠ 3, 5),respectively.