### Abstract

Original language | English |
---|---|

Title of host publication | Proc. XVII Encuentros de Geometría Computacional |

Place of Publication | Alicante, Spain |

Pages | 17-20 |

Number of pages | 4 |

Publication status | Published - 2017 |

### Cite this

*Proc. XVII Encuentros de Geometría Computacional*(pp. 17-20). Alicante, Spain.

**Bishellable drawings of $K_n$.** / Ábrego, B.M.; Aichholzer, O.; Fernández-Merchant, S.; McQuillan, D.; Mohar, B.; Mutzel, P.; Ramos, P.; Richter, R.B.; Vogtenhuber, B.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

*Proc. XVII Encuentros de Geometría Computacional.*Alicante, Spain, pp. 17-20.

}

TY - GEN

T1 - Bishellable drawings of $K_n$

AU - Ábrego, B.M.

AU - Aichholzer, O.

AU - Fernández-Merchant, S.

AU - McQuillan, D.

AU - Mohar, B.

AU - Mutzel, P.

AU - Ramos, P.

AU - Richter, R.B.

AU - Vogtenhuber, B.

PY - 2017

Y1 - 2017

N2 - In this work, we generalize the concept of $s$-shellability to bishellability, where the former implies the latter in the sense that every $s$-shellable drawing is, for any $b leq s-2$, also $b$-bishellable. Our main result is that $(lfloor n2 rfloor-2)$-bishellability also guarantees, with a simpler proof than for $s$-shellability, that a drawing has at least $H(n)$ crossings. We exhibit a drawing of $K_11$ that has $H(11)$ crossings, is 3-bishellable, and is not $s$-shellable for any $s$. This shows that we have properly extended the class of drawings for which the Harary-Hill Conjecture is proved.

AB - In this work, we generalize the concept of $s$-shellability to bishellability, where the former implies the latter in the sense that every $s$-shellable drawing is, for any $b leq s-2$, also $b$-bishellable. Our main result is that $(lfloor n2 rfloor-2)$-bishellability also guarantees, with a simpler proof than for $s$-shellability, that a drawing has at least $H(n)$ crossings. We exhibit a drawing of $K_11$ that has $H(11)$ crossings, is 3-bishellable, and is not $s$-shellable for any $s$. This shows that we have properly extended the class of drawings for which the Harary-Hill Conjecture is proved.

M3 - Conference contribution

SP - 17

EP - 20

BT - Proc. XVII Encuentros de Geometría Computacional

CY - Alicante, Spain

ER -