Results 1 
2 of
2
A LinearTime Algorithm for FourPartitioning FourConnected Planar Graphs (Extended Abstract)
 143
, 1997
"... Given a graph G = (V; E), k distinct vertices u 1 ; u 2 ; 1 1 1, u k 2 V and k natural numbers n 1 ; n 2 ; 1 1 1 ; n k such that P k i=1 n i = jV j, we wish to find a partition V 1 ; V 2 ; 1 1 1 ; V k of the vertex set V such that u i 2 V i , jV i j = n i , and V i induces a connected subgraph of G ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Given a graph G = (V; E), k distinct vertices u 1 ; u 2 ; 1 1 1, u k 2 V and k natural numbers n 1 ; n 2 ; 1 1 1 ; n k such that P k i=1 n i = jV j, we wish to find a partition V 1 ; V 2 ; 1 1 1 ; V k of the vertex set V such that u i 2 V i , jV i j = n i , and V i induces a connected subgraph of G for each i, 1 i k. Such a partition is called a k partition of G. The problem of finding a kpartition of a general graph is NPhard [DF85], and hence it is very unlikely that there is a polynomialtime algorithm to solve the problem. Although not every graph has a kpartition, Gyori and Lov'asz independently proved that every kconnected graph has a kpartition for any u 1 ; u 2 ; 1 1 1 ; u k and n 1 ; n 2 ; 1 1 1 ; n k [G78, L77]. However, their proofs do not yield any polynomialtime algorithm for actually finding a k ...
Efficient Algorithms for Drawing Planar Graphs
, 1999
"... x 1 Introduction 1 1.1 Historical Background . . .............................. 4 1.2 Drawing Styles . ................................... 4 1.2.1 Polyline drawings .............................. 5 1.2.2 Planar drawings ............................... 5 1.2.3 Straight line drawings ................. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
x 1 Introduction 1 1.1 Historical Background . . .............................. 4 1.2 Drawing Styles . ................................... 4 1.2.1 Polyline drawings .............................. 5 1.2.2 Planar drawings ............................... 5 1.2.3 Straight line drawings ............................ 6 1.2.4 Orthogonal drawings . . ........................... 7 1.2.5 Grid drawings ................................ 8 1.3 Properties of Drawings ................................ 9 1.4 Scope of this Thesis .................................. 10 1.4.1 Rectangular drawings . . . ......................... 11 1.4.2 Orthogonal drawings . . ........................... 12 1.4.3 Boxrectangular drawings ........................... 14 1.4.4 Convex drawings . . ............................. 16 1.5 Summary ....................................... 16 2 Preliminaries 20 2.1 Basic Terminology .................................. 20 2.1.1 Graphs and Multigraphs ........................... 20 i CO...