Location
Student Center
Document Type
Poster
Start Date
19-8-2025 1:30 PM
End Date
19-8-2025 2:30 PM
Description
The chromatic number, χ(G) of an undirected graph G=(V,E) is the minimum number of colors required to color its vertices so that no two adjacent vertices have the same color. Given a graph, G, finding its chromatic number is useful for solving scheduling problems and other combinatorial optimization problems. However, determining the chromatic number of a connected graph is NP-Hard, meaning there is no known polynomial time algorithm which solves it. Thus, we are interested in heuristic solutions which give approximations for the chromatic number in polynomial time. There are well-known heuristics for finding χ(G) for any graph G. In this project, we introduced modifications to the Welsh-Powell and the sequential heuristics. Specifically, for each vertex, we find its degree in the subgraph induced by the uncolored vertices, rather than using the whole graph throughout. We use numerical results to compare the efficiencies of these heuristics with their predecessors and other, non-iterative, constructive heuristics. We compare heuristics' runtimes and their average results, and we show the classes of graphs on which each of these heuristics is most effective.
Included in
Numerical Results of New and Modified Heuristics for the Vertex Coloring Problem
Student Center
The chromatic number, χ(G) of an undirected graph G=(V,E) is the minimum number of colors required to color its vertices so that no two adjacent vertices have the same color. Given a graph, G, finding its chromatic number is useful for solving scheduling problems and other combinatorial optimization problems. However, determining the chromatic number of a connected graph is NP-Hard, meaning there is no known polynomial time algorithm which solves it. Thus, we are interested in heuristic solutions which give approximations for the chromatic number in polynomial time. There are well-known heuristics for finding χ(G) for any graph G. In this project, we introduced modifications to the Welsh-Powell and the sequential heuristics. Specifically, for each vertex, we find its degree in the subgraph induced by the uncolored vertices, rather than using the whole graph throughout. We use numerical results to compare the efficiencies of these heuristics with their predecessors and other, non-iterative, constructive heuristics. We compare heuristics' runtimes and their average results, and we show the classes of graphs on which each of these heuristics is most effective.