The Königsberg bridge problem, solved by Leonhard Euler in 1735, is a seminal problem in graph theory. The problem asks whether it's possible to traverse all seven bridges in Königsberg (now Kaliningrad) exactly once.
Given a weighted graph and two vertices, find the shortest path between them. pearls in graph theory solution manual
Given a weighted graph, find a Hamiltonian cycle (a cycle visiting every vertex exactly once) with the minimum total edge weight. The Königsberg bridge problem, solved by Leonhard Euler
Given a weighted graph, find a subgraph that connects all vertices with the minimum total edge weight. The Königsberg bridge problem
Can we color the vertices of a planar graph with four colors such that no two adjacent vertices have the same color?