Series-parallel subgraphs of planar graphs

نویسندگان

  • Ehab S. Elmallah
  • Charles J. Colbourn
چکیده

In this paper we show that every 3-connected (3-edge-connected) planar graph contains a 2-connected (respectively, 2-edge-connected) spanning partial 2-tree (seriesparallel) graph. In contrast, a recent result by [4] implies that not all 3-connected graphs contain 2-edge-connected series-parallel spanning subgraphs.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Analogues of cliques for oriented coloring

We examine subgraphs of oriented graphs in the context of oriented coloring that are analogous to cliques in traditional vertex coloring. Bounds on the sizes of these subgraphs are given for planar, outerplanar, and series-parallel graphs. In particular, the main result of the paper is that a planar graph cannot contain an induced subgraph D with more than 36 vertices such that each pair of ver...

متن کامل

Partitioning the Edges of a Planar Graph into Two Partial K-Trees

In this paper we prove two results on partitioning the edges of a planar graph into two partial k-trees, for fixed values of k. Interest in this class of partitioning problems arises since many intractable graph and network problems admit polynomial time solutions on k-trees and their subgraphs (partial k-trees). The first result shows that every planar graph is a union of two partial 3-trees. ...

متن کامل

A special Class of Stochastic PERT Networks

Considering the network structure is one of the new approaches in studying stochastic PERT networks (SPN). In this paper, planar networks are studied as a special class of networks. Two structural reducible mechanisms titled arc contraction and deletion are developed to convert any planar network to a series-parallel network structure.&#10In series-parallel SPN, the completion time distribution...

متن کامل

A special Class of Stochastic PERT Networks

Considering the network structure is one of the new approaches in studying stochastic PERT networks (SPN). In this paper, planar networks are studied as a special class of networks. Two structural reducible mechanisms titled arc contraction and deletion are developed to convert any planar network to a series-parallel network structure. In series-parallel SPN, the completion time distribution f...

متن کامل

Shortest-Path Queries in Planar Graphs on GPU-Accelerated Architectures

We develop an efficient parallel algorithm for answering shortestpath queries in planar graphs and implement it on a multi-node CPU/GPU clusters. The algorithm uses a divide-and-conquer approach for decomposing the input graph into small and roughly equal subgraphs and constructs a distributed data structure containing shortest distances within each of those subgraphs and between their boundary...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Networks

دوره 22  شماره 

صفحات  -

تاریخ انتشار 1992