A simple certifying algorithm for 3-edge-connectivity
نویسندگان
چکیده
A linear-time certifying algorithm for 3-edge-connectivity is presented. Given a connected undirected graph G, if G 3-edge-connected, the generates construction sequence as positive certificate G. Otherwise, decomposes into its 3-edge-connected components and each of them well bridges cactus representation cut-pairs in negative certificates. All these are done by making only one pass over using an innovative contraction technique. Moreover, needs not be 2-edge-connected. The currently best-known more complicated it makes multiple passes uses involved reduction perturbation techniques rather than just basic graph-theoretic techniques.
منابع مشابه
A Self-stabilizing Algorithm For 3-Edge-Connectivity
Self-stabilization is a theoretical framework for fault-tolerance without external assistance. Adoption of self-stabilization in distributed systems has received considerable research interest over the last decade. In this paper, we propose a self-stabilizing algorithm for 3-edgeconnectivity of an asynchronous distributed model of computation. A self-stabilizing depth-first search algorithm is ...
متن کاملCertifying 3-Connectivity in Linear Time
One of the most noted construction methods of 3-vertex-connected graphs is due to Tutte and based on the following fact: Every 3-vertexconnected graph G on more than 4 vertices contains a contractible edge, i. e., an edge whose contraction generates a 3-connected graph. This implies the existence of a sequence of edge contractions from G to K4 such that every intermediate graph is 3-vertex-conn...
متن کاملA Certifying Algorithm for 3-Colorability of P5-Free Graphs
We provide a certifying algorithm for the problem of deciding whether a P5-free graph is 3-colorable by showing there are exactly six finite graphs that are P5-free and not 3-colorable and minimal with respect to this property.
متن کاملContractions, Removals, and Certifying 3-Connectivity in Linear Time
As existence result, it is well known that every 3-connected graph G = (V, E) on more than 4 vertices admits a sequence of contractions and a sequence of removal operations to K4 such that every intermediate graph in the sequences is 3-connected. We show that both sequences can be computed in linear time, improving the previous best known running time of O(|V |2) to O(|V | + |E|). This settles ...
متن کاملA Fast Algorithm for Optimally Increasing the Edge-Connectivity
Let G = (V, E ) be an undirected, unweighted graph with n nodes, m edges and connectivity A. Given an input parameter 6, the Edge Augmentation Problem is to find the smallest set of edges to add to G so that its edge-connectivity is increased by 6. In this paper we give a solution to this problem which runs in 0(J2nm + nF(n)) , where F ( n ) is the time to perform one maximum flow on G. In fact...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2023
ISSN: ['1879-2294', '0304-3975']
DOI: https://doi.org/10.1016/j.tcs.2023.113760