![Důležité termíny](https://cdn.muni.cz/media/3633704/image_2.jpg?mode=crop¢er=0.5,0.5&rnd=133572412150000000&heightratio=0.5&width=278)
Informace o publikaci
Bounded degree conjecture holds precisely for c-crossing-critical graphs with c<=12
Autoři | |
---|---|
Rok publikování | 2022 |
Druh | Článek v odborném periodiku |
Časopis / Zdroj | COMBINATORICA |
Fakulta / Pracoviště MU | |
Citace | |
www | |
Doi | http://dx.doi.org/10.1007/s00493-021-4285-3 |
Klíčová slova | Crossing number; Crossing-critical; Exhaustive generation; Path-width |
Popis | We study c-crossing-critical graphs, which are the minimal graphs that require at least c edge-crossings when drawn in the plane. For every fixed pair of integers with c >= 13 and d >= 1, we give first explicit constructions of c-crossing-critical graphs containing a vertex of degree greater than d. We also show that such unbounded degree constructions do not exist for c <=12, precisely, that there exists a constant D such that every c-crossing-critical graph with c <=12 has maximum degree at most D. Hence, the bounded maximum degree conjecture of c-crossing-critical graphs, which was generally disproved in 2010 by Dvorák and Mohar (without an explicit construction), holds true, surprisingly, exactly for the values c <=12. |
Související projekty: |