Introduction to Graph Theory · Problem 3.13

Multigraphs — Darij Grinberg

Mathematics — Graph Theory · eulerian-circuits-complete-graphs

Problem

Let

n

be a positive integer. Recall from Definition 2.6.1 (a) that

K_n

denotes the complete graph on

n

vertices. This is the graph with vertex set

V = \{1, 2, \ldots, n\}

and edge set

\mathcal{P}_2(V)

(so each two distinct vertices are adjacent). Find Eulerian circuits for the graphs

K_3

K_5

, and

K_7

. [Solution: This is Exercise 2 on homework set \#2 from my Spring 2017 course; see the course page for solutions.]