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Graph Algorithms Lab
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A lab that represents connections between objects as graphs and studies the structures and properties of those graphs through graph theory.
AboutAbout the lab
Capturing connections through mathematics to find good paths.
Professor Kenta Ozeki's lab studies graph theory, which investigates the structures and properties of graphs that model connections between objects.
Road networks and social media networks can be viewed as graphs.
The lab is particularly interested in good paths in graphs, and lists cycles, paths, and graph coloring as its research areas.
Hamiltonicity of graphs on closed surfaces is another of its research areas.
Key terms
- Graph
- A structure that represents connections between objects using vertices and edges. Road networks and social media networks are examples
- Hamiltonian cycle
- A cycle that passes through every vertex of a graph exactly once
ResearchResearch themes
A graph is a model of connections between objects, and road networks and social media networks can also be viewed as graphs. This lab studies the structures and properties of graphs, with a particular focus on good paths.
*Illustrative imageHamiltonicity of graphs on closed surfaces
A cycle that passes through every vertex of a graph exactly once is called a Hamiltonian cycle, and a path that does so is called a Hamiltonian path. The lab investigates whether these exist in graphs on closed surfaces.
*Illustrative imageGraph coloring
The lab lists graph coloring as a research area of graph theory, alongside cycles and paths. It has also published papers on graph coloring.
MembersFaculty
- ProfessorKenta Ozeki
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Queen's graph colouring” Bilorv / CC0 (cropped)
- Hamiltonicity of graphs on closed surfaces: “Cycle hamiltonien octaedre 2” Robert FERREOL / CC BY-SA 4.0 (cropped)
- Graph coloring: “Map coloring via graphs” Hmrussellmath / CC BY-SA 4.0 (cropped)
- Related lab (Algebra Lab (Shushi Harashita)): “De Long Room - DPLA - 4a293bd28e3b53c081af01f5355f855c” Brackett, J. Raymond / Public domain (cropped)
- Related lab (Probability Theory Lab (Masato Takei)): “Random walk 2000000” Purpy Pupple / CC BY-SA 3.0 (cropped)
- Related lab (Topological Graph Theory Lab): “Nauru-graph-on-torus-2” PSL27 / CC BY-SA 4.0 (cropped)
- Related lab (Otsuka Lab (Multimodal Information Processing Lab)): “Eye-tracking setup” Naomi Nota / CC BY-SA 2.0 (cropped)
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