Map Coloring, Polyhedra, and the Four-color Problem |
Contents
PREFACE | 1 |
CHAPTER TWO EULERS EQUATION | 20 |
CHAPTER THREE HAMILTONIAN CIRCUITS | 52 |
Copyright | |
7 other sections not shown
Common terms and phrases
3-coloring 3-connected 3-polyhedral 3-valent map 3-valent polyhedron 4-sided 5-valent neighbors 5-valent vertex argument called Chapter colony pair coloring problems complete graph connected graph contain corresponding coun countries meet dual graph duality edges colored equivalent form Euler characteristic Euler's equation example Exercise exist fewer colors fewer edges fewer vertices four Four-Color Conjecture four-color problem Four-Color Theorem graph G Hamiltonian circuit handle body hedron implies inequality infinite number irreducible graph irreducible maps joined Kempe chain label least three edges loops map coloring map in Figure map is four-colorable map requiring Math mathematics minimum number multiple edges multiple of three number of colors number of countries number of edges number of marks number of vertices original graph original map planar graph plane proper map prove reducible configurations requiring five colors sphere strongly reducible Suppose tetrahedron three colors tices torus truncate unavoidable set v₁ vertices of valence