Euler Tours
Neeldhara Misra
DSA1 Week 4
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Work through the exercises in the Mathigon lesson
about the Bridges of Königsberg
A walk is a sequence of edges
\(e_1, \ldots, e_{n-1}\)
such that there exists a sequence of vertices
\(v_1, \ldots, v_n\)
for which \(e_i = (v_i, v_{i+1})\)
for all \(1 \leqslant i \leqslant n-1\).
An (closed/open) Euler Tour of a graph \(G\)
is a (closed/open) walk
that contains every edge exactly once
(i.e, no repeats and no omissions).
If a graph \(G\) has:
(a) more than two vertices of odd degree, or
(b) exactly one vertex of odd degree, then
it does not have an Euler Tour of any kind
(closed or open).
What we discovered
If a graph \(G\) has:
(a) exactly two vertices of odd degree, or
(b) no vertex of odd degree, then
does it have an Euler Tour of some kind
(closed or open)?
Food for thought