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...

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...

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...

_{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...

In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain...

bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the...

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....

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

of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are...

Rounding Algorithm for CorrelationClustering on Complete and Complete k-partite Graphs". Proceedings of the 46th Annual ACM on Symposium on Theory of Computing...

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...

is the chromatic index of G; and Kn,n, the complete bipartite graph with equal partite sets. The most famous open problem about list edge-coloring is...

{\mathcal {K}}_{j}({\mathcal {G}}^{(1)})=K_{l}^{(j)}(V_{1},\ldots ,V_{l})} is a complete l {\displaystyle l} -partite j {\displaystyle j} -graph. The following...

condition is not necessary, because the labels of vertices of one partite set in a bipartite graph can be rearranged arbitrarily. In 1962 Ford and Fulkerson gave...

extends this result to H = Kr(t), the complete r-partite graph with t vertices in each class, which is the graph obtained by taking Kr and replacing each vertex...

1-{\frac {1}{r-1}}} , this gives a graph that is ( r − 1 ) {\displaystyle (r-1)} -partite and hence gives no K r {\displaystyle K_{r}} s. The lower bound was...

In graph theory, the graph removal lemma states that when a graph contains few copies of a given subgraph, then all of the copies can be eliminated by...

In graph theory, boxicity is a graph invariant, introduced by Fred S. Roberts in 1969. The boxicity of a graph is the minimum dimension in which a given...

hyperedge contains exactly one vertex of each set (so a 2-partite hypergraph is a just bipartite graph). Let n be any positive integer. Any family of rn – r...

T ( n , r ) {\displaystyle T(n,r)} is the Turán graph: a complete r {\displaystyle r} -partite graph on n {\displaystyle n} vertices, with vertices distributed...

Georgakopoulos, Agelos; Sprüssel, Philipp (2009-01-01). "Perfect matchings in r-partite r-graphs". European Journal of Combinatorics. 30 (1): 39–42. arXiv:0911.4008...

In graph theory, the sphericity of a graph is a graph invariant defined to be the smallest dimension of Euclidean space required to realize the graph as...

subgraph Bollobás, Béla (2004), "VI.2 Complete subgraphs of r-partite graphs", Extremal Graph Theory, Mineola, NY: Dover Publications Inc., pp. 309–326,...

discipline of graph theory, a 3-dimensional matching is a generalization of bipartite matching (also known as 2-dimensional matching) to 3-partite hypergraphs...

is at most k {\displaystyle k} , so H ( s , r ) ≤ k {\displaystyle H(s,r)\leq k} . Example neighborhood structures for problems on graphs: Swap - A partition...

S2CID 40920263. Sperfeld, Konrad (2013), "On the page number of complete odd-partite graphs", Discrete Mathematics, 313 (17): 1689–1696, doi:10.1016/j.disc.2013...

\mathbb {Z} /M\mathbb {Z} } . We will construct a k {\displaystyle k} -partite ( k − 1 ) {\displaystyle (k-1)} -uniform hypergraph G {\displaystyle G} from...

\ldots ,n_{k}}} is a "chessboard complex" defined for a k-dimensional chessboard. Equivalently, it is the set of matchings in a complete k-partite hypergraph...

In graph theory, a matching in a hypergraph is a set of hyperedges, in which every two hyperedges are disjoint. It is an extension of the notion of matching...