## Implementation and Analysis of Efficient Graph Planarity Testing Algorithms |

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### Contents

Preliminary Notions | 8 |

Testing Planarity for Arbitrary Graphs | 19 |

Testing Planarity for Special Graphs | 42 |

3 other sections not shown

### Common terms and phrases

adjacent algorithm CC algorithm terminates American Mathematical Society analysis Apply algorithm array Beineke bridge of G C0MP chain decomposition Complete Graph computing connected components contains contour of F cycle-chain decomposition DATA(NEXT Delete Edge bridge edges incident elementary chain elementary cycle F of G face F face of G FACE(KFAC Figure flowchart for algorithm FORTRAN Frank Harary Free vertex G is planar G relative go to step Goldstein's algorithm graph G Graph Theory I0RD Implementation flowchart Incidence Matrix INDX initial cycle Journal of Mathematics K0MP KFAC KURR L0CL LADJ LADJ(I LADJ(VERI LCHA Let G LINK(NEXT list representation LNEW Mark method NATT NCYC NEDG NEIB NFAC NSTK number of edges number of vertices NVER PL/I Planar Graphs planar representation planarity tests representation of G return to step Section simple biconnected graph simple graph subgraph testing the planarity Theorem Tutte unplaced VATT VERT VERW VRTX