Graph families | Graph coloring

Critical graph

In graph theory, a critical graph is an undirected graph all of whose subgraphs have smaller chromatic number. In such a graph, every vertex or edge is a critical element, in the sense that its deletion would decrease the number of colors needed in a graph coloring of the given graph. The decrease in the number of colors cannot be by more than one. (Wikipedia).

Critical graph
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Brooks' theorem | Graph theory | Hajós construction | Chromatic number | Regular graph | De Bruijn–Erdős theorem (graph theory) | Cycle graph | Complete graph | Factor-critical graph | Glossary of graph theory | Degree (graph theory) | Critical path method | K-edge-connected graph | Graph coloring