## Cycles and colourings '97: proceedings of the 6th Workshop on Cycles and Colourings, Stará Lesná, September 7-12, 1997 |

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### Contents

A note on a conjecture concerning tree | 15 |

The 10cycle C10 is light in the family of all plane trian | 35 |

On an Eberhardtype problem in cubic polyhedral graphs | 57 |

2 other sections not shown

### Common terms and phrases

0/1-neighbourhood 1-saturated 3-connected additive hereditary properties adjacent B2 has saturated B2 inside 4-cycle big otherwise boundary vertices Bratislava Cartesian products claw-free colour component of G connected 3-regular consider contains a vertex contradiction crossing numbers cubic polyhedral graph cycle in Dm define deg(Aj degG(x degree at least denote digraph dual graph E-mail edge of G exists fair partition Fjgure fractional chromatic full fragment G E(G G F(G G V(G graph G graph obtained graph properties Graph Theory gs(P gs(R hamiltonian cycle hamiltonian graphs hypergraph implies induced subgraph inside 3-cycle integer irreducible JENDROL Košice Lemma Let G light 10-cycle Mathematical Publications maximal planar graph minimum degree Moreover multiple edge neighbour of B2 non-hamiltonian partition of G path proof of Theorem proved Rules saturated 0-neighbours Slovak Slovakia strongly connected subcase Subject Classification 1991 subsets suppose Tatra Mt tonian uniquely partitionable graphs vertex of degree Xp(G y^xj