Neeldhara Misra

# DSA1 Week 4

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Work through the exercises in the Mathigon lesson

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

#### 2023 DSA1 | Week 4

By Neeldhara Misra

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