Graph coloring
Graph coloring is the assignment of colors to graph elements subject to constraints, such as requiring adjacent vertices to have different colors.
Fabulous Adventures in Data Structures and Algorithms
Graph coloring is the assignment of colors to graph elements subject to constraints such as adjacent vertices receiving different colors.
- How it is used
- Models incompatible assignments as edges between nodes that must receive different colors.
- How deep it goes
- Develops a recursive C# algorithm and backtracking strategy, then explains worst-case complexity without proving NP-completeness.
- Examples
- Uses a South America map, a Sudoku grid, and gate, classroom, and register-allocation scenarios.
- What you can do after
- Build it from scratch with an immutable C# graph and choose between low-degree recursion and backtracking search.
Read how Fabulous Adventures in Data Structures and Algorithms explains graph coloring →
Advanced Algorithms and Data Structures
Graph coloring is the assignment of colors to graph vertices subject to specified restrictions on the colors of adjacent vertices.
- How it is used
- Uses two-coloring to test bipartiteness while recognizing the forbidden graph K3,3 in planarity analysis.
- How deep it goes
- Develops a BFS-based implementation with a queue, color table, conflict test, and partition output, but omits complexity analysis.
- Examples
- Uses two-colorable and non-two-colorable graphs, plus K3,3 recognition requiring partitions of size three.
- What you can do after
- Diagnose bipartiteness with BFS and recover the two vertex partitions when coloring succeeds.
Read how Advanced Algorithms and Data Structures explains graph coloring →
Related concepts
- np-complete problemkind of · An NP-complete problem is a decision problem in NP to which every problem in NP can be reduced in polynomial time.
- bipartite graphequivalent to · A bipartite graph is a graph whose vertices can be partitioned into two disjoint sets, with edges only between the sets.
- backtrackingaddressed by · Backtracking is a technique that returns to earlier decisions or states along a path to reconsider choices, explore alternatives, or reconstruct a solution.
- recursionaddressed by · Recursion is a computational technique in which a definition or procedure refers to or invokes the same definition or procedure, directly or indirectly.
These guides are generated from the text of Manning books by Manning's knowledge graph and link to the sections they draw on. The full books are available on liveBook and at manning.com.