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Overfull graph
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Overfull graph : ウィキペディア英語版
Overfull graph
In graph theory, an overfull graph is a graph whose size is greater than the product of its maximum degree and half of its order floored, i.e. |E| > \Delta (G) \lfloor |V|/2 \rfloor where |E| is the size of ''G'', \displaystyle\Delta(G) is the maximum degree of ''G'', and |V| is the order of ''G''. The concept of an overfull subgraph, an overfull graph that is a subgraph, immediately follows. An alternate, stricter definition of an overfull subgraph S of a graph G requires \displaystyle\Delta (G) = \Delta (S).
==Properties==
A few properties of overfull graphs:
# Overfull graphs are of odd order.
# Overfull graphs are class 2. That is, they require at least colors in any edge coloring.
# A graph ''G'', with an overfull subgraph ''S'' such that \displaystyle\Delta (G) = \Delta (S), is of class 2.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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