Turán Numbers of Vertex-disjoint Cliques in r-Partite Graphs

Cohen-Macaulay $r$-partite graphs with minimal clique cover

‎In this paper‎, ‎we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is Cohen-Macaulay‎. ‎It is proved that if there exists a cover of an $r$-partite Cohen-Macaulay graph by disjoint cliques of size $r$‎, ‎then such a cover is unique‎.

Turán numbers of vertex-disjoint cliques in -partite graphs

Polar cographs

Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s, k)-polar if there exists a partition A, B of its vertex set such that A induces a complete s-partite graph (i.e., a collection of at most s disjoint stable sets with complete links between all sets) and B a disjoint union of at most k cliques (i....

2 2 N ov 2 00 7 Graphs with many r - cliques have large complete r - partite subgraphs

Let r ≥ 2 and c > 0. Every graph on n vertices with at least cnr cliques on r vertices contains a complete r-partite subgraph with r − 1 parts of size ⌊cr log n⌋ and one part of size greater than n1−c r−1 . This result implies the Erdős-Stone-Bollobás theorem, the essential quantitative form of the Erdős-Stone theorem.

Some Algebraic and Combinatorial Properties of the Complete $T$-Partite Graphs

In this paper, we characterize the shellable complete $t$-partite graphs. We also show for these types of graphs the concepts vertex decomposable, shellable and sequentially Cohen-Macaulay are equivalent. Furthermore, we give a combinatorial condition for the Cohen-Macaulay complete $t$-partite graphs.