منابع مشابه
Rooted Cycle Bases
A cycle basis in an undirected graph is a minimal set of simple cycles whose symmetric differences include all Eulerian subgraphs of the given graph. We define a rooted cycle basis to be a cycle basis in which all cycles contain a specified root edge, and we investigate the algorithmic problem of constructing rooted cycle bases. We show that a given graph has a rooted cycle basis if and only if...
متن کاملOn robust cycle bases
Two types of robust cycle bases are defined via recursively nice arrangements; complete and bipartite complete graphs are shown to have such bases. It is shown that a diagram in a groupoid is commutative up to natural equivalence (cutne) if for each cycle in a robust basis of the graph underlying the diagram, the composition of the morphisms is naturally equivalent to the identity. For a hyperc...
متن کاملConvex Cycle Bases
Convex cycles play a role e.g. in the context of product graphs. We introduce convex cycle bases and describe a polynomial-time algorithm that recognizes whether a given graph has a convex cycle basis and provides an explicit construction in the positive case. Relations between convex cycles bases and other types of cycles bases are discussed. In particular we show that if G has a unique minima...
متن کاملOn finding cycle bases and fundamental cycle bases with a shortest maximal cycle
An undirected biconnected graph G with nonnegative integer lengths on the edges is given. The problem we consider is that of finding a cycle basis B of G such that the length of the longest cycle included in B is the smallest among all cycle bases of G. We first observe that Horton’s algorithm [SIAM J. Comput. 16 (2) (1987) 358–366] provides a fast solution of the problem that extends the one g...
متن کاملPure-cycle Hurwitz factorizations and multi-noded rooted trees
Pure-cycle Hurwitz number counts the number of connected branched covers of the projective lines where each branch point has only one ramification point over it. The main result of the paper is that when the genus is 0 and one of the ramification indices is d, the degree of the covers, the pure-cycle Hurwitz number is dr−3, where r is the number of branch points. Springer and Irving independent...
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ژورنال
عنوان ژورنال: Journal of Graph Algorithms and Applications
سال: 2017
ISSN: 1526-1719
DOI: 10.7155/jgaa.00434