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- W3149822771 abstract "In this paper, the cycle’s structure of embedded graphs in surfaces are studied. According to the method of fundamental cycles, the set C(C contains all shortest) is found. A undirected graph G with n vertices has at most O(n5) many shortest cycles; If the shortest cycle of G is odd cycle, then G has at most O(n3) many shortest cycles; If G has been embedded in a surface Sg(Ng, g is a constant), then it has at most O(n3) shortest cycles, moreover, if the shortest cycle of G is odd cycle, then, G has at most O(n2) many shortest cycles. We can find a cycle base of G, the number of odd cycles of G, the number of even cycles of G, the number of contractible cycles of G, the number of non-contractible cycles of G, are all decided. If the Π-embedded graph G has Π-twosided cycles, then,C contains a shortest Π-twosided cycle of G, there is a polynomially bounded algorithm that finds a shortest Π-twosided cycle of a Π-embedded graph G, the new and simple solutions about the open problem of Bojan Mohar and Carsten Thomassen are obtained." @default.
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- W3149822771 date "2015-01-01" @default.
- W3149822771 modified "2023-09-26" @default.
- W3149822771 title "The Cycle＇s Structure of Embedded Graphs in Surfaces" @default.
- W3149822771 hasPublicationYear "2015" @default.
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