Abstract
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.
Original language | English |
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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 |