The Four-color Problem: Assaults and Conquest |
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Page 99
... equivalent formulations are true . In other words , the many imaginative equivalent formulations in other apparently far - fetched domains were correctly conceived . The intuition and reasoning involved were right . Of course , shifting ...
... equivalent formulations are true . In other words , the many imaginative equivalent formulations in other apparently far - fetched domains were correctly conceived . The intuition and reasoning involved were right . Of course , shifting ...
Page 113
... equivalent to Conjecture C4 since a one- factorization is equivalent to an edge - coloring . An interesting variant on this conjecture is given in Ore ( 1967 , p . 103 ) . Conjecture C11 Every bridgeless planar graph is the union of ...
... equivalent to Conjecture C4 since a one- factorization is equivalent to an edge - coloring . An interesting variant on this conjecture is given in Ore ( 1967 , p . 103 ) . Conjecture C11 Every bridgeless planar graph is the union of ...
Page 129
... equivalent . n PROOF Consider two arrangements of the n - fold sum a1 + + an . Extend the analogous two n - admissible sets to make them complete - say { ( Pi , Qi ) | 1 ≤ i ≤s } and { ( pí , q¦ ) | ≤ i ≤ s } . If Conjecture C20 ...
... equivalent . n PROOF Consider two arrangements of the n - fold sum a1 + + an . Extend the analogous two n - admissible sets to make them complete - say { ( Pi , Qi ) | 1 ≤ i ≤s } and { ( pí , q¦ ) | ≤ i ≤ s } . If Conjecture C20 ...
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