What is the history of graph theory?

Graph theory is a branch of mathematics studying graphs, which model pairwise relations between objects using vertices and edges. Research in this field has historically intersected with problems like the four color theorem, which spurred early investigations into graph coloring. Over time, specialized areas such as extremal graph theory and the study of snarks emerged to address complex structural properties.

What we know

• Graph theory is the mathematical study of graphs, which consist of vertices connected by edges to model pairwise relations. [1, 2]
• Research on snarks originated in Peter G. Tait's work on the four color theorem in 1880. [5]
• Dénes Kőnig proved Kőnig's theorem in 1931, describing an equivalence between maximum matching and minimum vertex cover problems in bipartite graphs. [4]

Where to go next

• a case in pointWhat are snarks in graph theory?
• the bigger pictureHow does extremal graph theory work?
• whoWho was Dénes Kőnig?
• how we knowWhat is Kőnig's theorem?
• compared withHow are directed and undirected graphs different?
• an unexpected connectionHow did Martin Gardner name snarks?Although research on snarks began with Peter G. Tait in 1880, the name itself was given much later by Martin Gardner in 1976.

Sources

• [1]graph theory (Wikidata Q131476) · CC0 1.0
• [2]Graph theory · CC BY-SA 4.0
• [3]Extremal graph theory · CC BY-SA 4.0
• [4]Kőnig's theorem (graph theory) · CC BY-SA 4.0
• [5]Snark (graph theory) · CC BY-SA 4.0