In graph theory, a part of mathematics, a k-partite graph is a graph whose vertices are (or can be) partitioned into k different independent sets. Equivalently...

graph is 4-colorable (i.e., 4-partite). Fáry's theorem states that every simple planar graph admits a representation as a planar straight-line graph....

generalized to k-partite graphs and graphs that avoid larger cliques as subgraphs in Turán's theorem, and these two complete bipartite graphs are examples...

graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject...

mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful...

Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...

and balanced. k {\displaystyle k} -uniform - each hyperedge contains precisely k {\displaystyle k} vertices. k {\displaystyle k} -partite - the vertices...

_{i=1}^{k}n_{i}}}\sum _{i=1}^{k}{n_{i}H(G_{i})}} . Additionally, simple formulas exist for certain families classes of graphs. Complete balanced k-partite graphs...

formed as subgraphs of these complete bi-partite graphs in certain cases. Subgraphs of complete bipartite graphs Km,n exist when m and n share a factor...

meta-category, multicategory, and multi-graph, k-partite graph, or colored graph (see a color figure, and also its definition in graph theory). Supercategories were...