3 papers
math.CO2016
Steinberg's Conjecture is false
Vincent Cohen-Addad, Michael Hebdige, Daniel Kral +2
Steinberg conjectured in 1976 that every planar graph with no cycles of length four or five is 3-colorable. We disprove this conjecture.
math.CO2016
Cyclic Coloring of Plane Graphs with Maximum Face Size 16 and 17
Zdenek Dvorak, Michael Hebdige, Filip Hlasek +2
Plummer and Toft conjectured in 1987 that the vertices of every 3-connected plane graph with maximum face size D can be colored using at most D+2 colors in such a way that no face…
math.CO2015
Third case of the Cyclic Coloring Conjecture
Michael Hebdige, Daniel Kral
The Cyclic Coloring Conjecture asserts that the vertices of every plane graph with maximum face size D can be colored using at most 3D/2 colors in such a way that no face is incide…