The Four-color Problem: Assaults and Conquest |
From inside the book
Results 1-3 of 49
Page 11
... pair [ s , s ' ] is the equival- ence class of an ordered pair ( s , s ' ) under the relation [ s , s ' ] = [ s ' , s ] . The only difference between these unordered pairs and the sets with two elements is that [ s , s ] is an unordered ...
... pair [ s , s ' ] is the equival- ence class of an ordered pair ( s , s ' ) under the relation [ s , s ' ] = [ s ' , s ] . The only difference between these unordered pairs and the sets with two elements is that [ s , s ] is an unordered ...
Page 128
... pair of parentheses in the arrangement encloses a sequence a , ++ a ,, and we associate to this pair of parentheses the ordered pair ( r — 1 , s ) . It is easy to check that the set of all ordered pairs corresponding to the various related ...
... pair of parentheses in the arrangement encloses a sequence a , ++ a ,, and we associate to this pair of parentheses the ordered pair ( r — 1 , s ) . It is easy to check that the set of all ordered pairs corresponding to the various related ...
Page 157
... pair if H is a full subgraph of G. ( Note that if H = 2 , then H is always full in G. ) If c is an r - coloring of G in which all r colors are used , we write | c = r . If ( G , H ) is a pair of graphs , c is a coloring of G , and d a ...
... pair if H is a full subgraph of G. ( Note that if H = 2 , then H is always full in G. ) If c is an r - coloring of G in which all r colors are used , we write | c = r . If ( G , H ) is a pair of graphs , c is a coloring of G , and d a ...
Contents
Historical Setting | 3 |
Problems and Methods | 21 |
Solution of the FourColor Problem | 52 |
Copyright | |
5 other sections not shown
Other editions - View all
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