|
In mathematics, and particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting two points by an edge whenever the distance between the two points is exactly one. Edges of unit distance graphs sometimes cross each other, so they are not always planar; a unit distance graph without crossings is called a matchstick graph. The Hadwiger–Nelson problem concerns the chromatic number of unit distance graphs. It is known that there exist unit distance graphs requiring four colors in any proper coloring, and that all such graphs can be colored with at most seven colors. Another important open problem concerning unit distance graphs asks how many edges they can have relative to their number of vertices. ==Examples== The following graphs are unit distance graphs: * Any cycle graph * Any grid graph * Any hypercube graph * Any star graph * The Petersen graph * The Heawood graph * The wheel graph ''W''7 * The Moser spindle, the smallest 4-chromatic unit distance graph 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「unit distance graph」の詳細全文を読む スポンサード リンク
|