König's line coloring theorem states that the edge chromatic number of any bipartite graph equals its maximum vertex degree. In other words, every bipartite graph is a class 1 graph.
König's Line Coloring Theorem
See also
Bipartite Graph, Edge Chromatic Number, König-Egeváry Theorem, König's TheoremExplore with Wolfram|Alpha
References
Biggs, N. L.; Lloyd, E. K.; and Wilson, R. J. Graph Theory 1736-1936. Oxford University Press, pp. 203-207, 1976.Kőnig, D. "Gráfok és alkalmazásuk a determinánsok Žs a halmazok elméletére." Matematikai és Természettudományi Értesítő 34, 104-119, 1916.Lovász, L. and Plummer, M. D. Matching Theory. New York: North-Holland, p. 37, 1986.Cite this as:
Weisstein, Eric W. "König's Line Coloring Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KoenigsLineColoringTheorem.html