The Four-color Problem: Assaults and Conquest |
Contents
Historical Setting | 3 |
Problems and Methods | 21 |
Solution of the FourColor Problem | 52 |
Copyright | |
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The Four-color Problem: Assaults and Conquest Thomas L. Saaty,Paul C. Kainen No preview available - 1986 |
Common terms and phrases
Academic Press adjacent bipartite boundary C₁ called chain group Chromatic Number chromatic polynomials chromials chromodendron cographic coloring of G Combinatorial complete graph components connected graph Corollary corresponding cubic graph cubic map D-reducible define denote disjoint dual dual graph edges of G embedded endpoints equivalent Euler's formula example Figure finite five-color following theorem Four Color Problem four-color conjecture four-color theorem four-coloring of G G contains G is planar G₁ G₂ graph G Graph Theory Graphen hamiltonian circuit Heawood Hence homeomorphic induced integer isomorphic k-colorable Kempe chains Kempe residues Lemma Let G Mathematics maximal planar graph minimum number neighbors number of colors number of edges number of vertices obtained pair partition plane PROOF Let prove reducible configurations regions result subgraph of G subset Suppose surface sw(G Tait-coloring three-colored topological tree triangulation Tutte unavoidable set v₁ v₂ vertex of degree Whitney