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math.CO2015
10-tough chordal graphs are Hamiltonian
Adam Kabela, Tomáš Kaiser
Chen et al. proved that every 18-tough chordal graph has a Hamilton cycle [Networks 31 (1998), 29-38]. Improving upon their bound, we show that every 10-tough chordal graph is Hami…
math.CO2015★ 3 cited
Planar graphs have two-coloring number at most 8
Zdeněk Dvořák, Adam Kabela, Tomáš Kaiser
We prove that the two-colouring number of any planar graph is at most 8. This resolves a question of Kierstead et al. [SIAM J. Discrete Math.~23 (2009), 1548--1560]. The result is…