The Four-color Problem: Assaults and Conquest |
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Page 28
... given number of colors . Now we turn the problem around and ask : " What is the minimum number of colors required for coloring the vertices of any graph ? " Can the answer be given in terms of the properties of the particular graph ...
... given number of colors . Now we turn the problem around and ask : " What is the minimum number of colors required for coloring the vertices of any graph ? " Can the answer be given in terms of the properties of the particular graph ...
Page 91
... given above and ( R ) ≤ 1 , then R is likely to be D - reducible . We would like to apply our assumption to an arbitrary R with ≤ 1. But then the problem is to know whether or not R contains a reduction obstacle . The first step in ...
... given above and ( R ) ≤ 1 , then R is likely to be D - reducible . We would like to apply our assumption to an arbitrary R with ≤ 1. But then the problem is to know whether or not R contains a reduction obstacle . The first step in ...
Page 180
... given by W ( e ) = ê where ê is the orthogonal edge to e ( see the definition of D ( M ) in Sec . 1-2 ) . By ... given are nice theoretically but may be difficult to apply and slow to yield results . In general , given any finite problem ...
... given by W ( e ) = ê where ê is the orthogonal edge to e ( see the definition of D ( M ) in Sec . 1-2 ) . By ... given are nice theoretically but may be difficult to apply and slow to yield results . In general , given any finite problem ...
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