14.4: Summary
- Page ID
- 60146
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- Vizing’s Theorem
- Graphs are bipartite if and only if they contain no cycle of odd length
- Ramsey’s Theorem
- Graphs are bipartite if and only if they are \(2\)-colourable
- Brooks’ Theorem
- Petersen graph
- Important Definitions:
- Proper \(k\)-edge-colouring, \(k\)-edge-colourable
- Edge chromatic number, chromatic index
- Class one graph, class two graph
- Bipartite, bipartition
- Complete bipartite graph
- Proper \(k\)-colouring, \(k\)-colourable
- Chromatic number
- \(k\)-critical
- Notation:
- \(χ'(G)\)
- \(K_{m,n}\)
- \(R(n_1, . . . , n_c)\)
- \(χ(G)\)