دانلود گزارش کارورزی و کار آموزی

چکیده : 

A geometric graph is rational if all its edges have rational lengths. In 2008 M. Kleber asked

for what graph the vertices can be slightly perturbed in their ϵ-neighborhoods in such a

way that the resulting graph becomes rational (the ϵ-approximation) and in addition the

vertices can have rational coordinates (the rational ϵ-approximation). J. Geelen et al. in

2008 proved that any geometric cubic graph has a rational ϵ-approximation for any ϵ > 0.

In 2011 A. Dubickas assumed the existence of up to four vertices of degree above 3. We

prove that any connected geometric graph with maximum degree 4 and a vertex w of

degw < 4 and any 3-tree have ϵ-rational approximations for any ϵ > 0.