On building 4-critical plane and projective plane multiwheels from odd wheels

2012/02/22 by Dainis Zeps, Zeps, Dainis
Engineering · Mathematics · #Combinatorics (math.CO) #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Mechanical Engineering and Vibrations Research #Robotic Mechanisms and Dynamics #math.CO

paper · pdf · doi:10.48550/arxiv.1202.4862

10 pages

arxiv created 2012/02/22 · openalex publication_date 2012/02/22 · arxiv updated 2012/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We build unbounded classes of plane and projective plane multiwheels that are 4-critical that are received summing odd wheels as edge sums modulo two. These classes can be considered as ascending from single common graph that can be received as edge sum modulo two of the octahedron graph O and the minimal wheel W3. All graphs of these classes belong to 2n-2-edges-class of graphs, among which are those that quadrangulate projective plane, i.e., graphs from Grötzsch class, received applying Mycielski's Construction to odd cycle.

Related

• 4-critical wheel graphs of higher order
• Reducing quadrangulations of the sphere and the projective plane
• Francis Guthrie's approach to The Four Color Problem
• Odd wheels are not odd-distance graphs
• Cycles, wheels, and gears in finite planes