منابع مشابه
Certifying 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 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 کاملOn the edge-connectivity of C_4-free graphs
Let $G$ be a connected graph of order $n$ and minimum degree $delta(G)$.The edge-connectivity $lambda(G)$ of $G$ is the minimum numberof edges whose removal renders $G$ disconnected. It is well-known that$lambda(G) leq delta(G)$,and if $lambda(G)=delta(G)$, then$G$ is said to be maximally edge-connected. A classical resultby Chartrand gives the sufficient condition $delta(G) geq frac{n-1}{2}$fo...
متن کاملEdge-connectivity and super edge-connectivity of P2-path graphs
For a graph G, the P2-path graph, P2(G), has for vertices the set of all paths of length 2 in G. Two vertices are connected when their union is a path or a cycle of length 3. We present lower bounds on the edge-connectivity, (P2(G)) of a connected graph G and give conditions for maximum connectivity. A maximally edge-connected graph is superif each minimum edge cut is trivial, and it is optimum...
متن کاملOn the 3-restricted edge connectivity of permutation graphs
An edge cut W of a connected graph G is a k-restricted edge cut if G−W is disconnected, and every component of G −W has at least k vertices. The k-restricted edge connectivity is defined as the minimum cardinality over all k-restricted edge cuts. A permutation graph is obtained by taking two disjoint copies of a graph and adding a perfect matching between the two copies. The k-restricted edge c...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2015
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-015-0075-x