Finding Even Cycles Even Faster
نویسندگان
چکیده
We describe efficient algorithms for finding even cycles in undirected graphs. Our main results are the following: (i) For every k ≥ 2, there is an O(V ) time algorithm that decides whether an undirected graph G = (V,E) contains a simple cycle of length 2k and finds one if it does. (ii) There is an O(V ) time algorithm that finds a shortest even cycle in an undirected graph G = (V,E).
منابع مشابه
A Faster Algorithm for the Maximum Even Factor Problem
Given a digraph G = (V G,AG), an even factor M ⊆ AG is a subset of arcs that decomposes into a collection of node-disjoint paths and even cycles. Even factors in digraphs were introduced by Geleen and Cunningham and generalize path matchings in undirected graphs. Finding an even factor of maximum cardinality in a general digraph is known to be NP-hard but for the class of odd-cycle symmetric di...
متن کاملFinding k Simple Shortest Paths and Cycles
We present algorithms and hardness results for several problems related to finding multiple simple shortest paths in a graph. Our main result is a new algorithm for finding k simple shortest paths for all pairs of vertices in a weighted directed graph G = (V,E). For k = 2 our algorithm runs in O(mn + n logn) time where m and n are the number of edges and vertices in G. Our approach is based on ...
متن کامل0n removable cycles in graphs and digraphs
In this paper we define the removable cycle that, if $Im$ is a class of graphs, $Gin Im$, the cycle $C$ in $G$ is called removable if $G-E(C)in Im$. The removable cycles in Eulerian graphs have been studied. We characterize Eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for Eulerian graph to have removable cycles h...
متن کاملBenefits of p-Cycles in a Mixed Protection and Restoration Approach
There are reasons to expect that the protection switching times of p-cycles will allow them to be considered for protecting services where previously only 1+1 automatic protection switching would have been specified, for the highest speed. Here we introduce p-cycles as an option in a mixedmethod environment to protect demands that do not strictly require dedicated 1+1 APS, but need a faster swi...
متن کاملUlnar Collateral Ligament Reconstruction Versus Repair With Internal Bracing: Comparison of Cyclic Fatigue Mechanics
Background Ulnar collateral ligament (UCL) injuries have increased significantly in recent years, and reconstruction has become the preferred treatment for UCL injury over ligament repair. In a recent study, UCL repair with internal bracing demonstrated significantly greater resistance to gap formation in biomechanical tests, even at low cycles of valgus loading. Purpose/Hypothesis The purpos...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 10 شماره
صفحات -
تاریخ انتشار 1994