Startseite Mathematik The influence of separating cycles in drawings of K5 ∖ e in the join product with paths and cycles
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The influence of separating cycles in drawings of K5e in the join product with paths and cycles

  • Michal Staš EMAIL logo und Mária Timková
Veröffentlicht/Copyright: 15. Oktober 2024
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Abstract

The crossing number cr(H) of a graph H is the minimum number of edge crossings over all drawings of H in the plane. Let H be the connected graph of order five isomorphic to K5e obtained by removing one edge from the complete graph K5. The main aim of the paper is to give the crossing numbers of the join products H + Pn and H + Cn, where Pn and Cn are the path and the cycle on n vertices, respectively. The proofs are done with the help of a suitable classification of a large number of drawings of the graph H in view of the existence of a separating cycle of two possible types.

  1. Communicated by Peter Horák

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Received: 2023-10-26
Accepted: 2024-03-15
Published Online: 2024-10-15
Published in Print: 2024-10-28

© 2024 Mathematical Institute Slovak Academy of Sciences

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