Complete subgraphs of the graphs of convex polytopes
نویسندگان
چکیده
منابع مشابه
Complete subgraphs of random graphs
A classical theorem by Erdős, Kleitman and Rothschild on the structure of triangle-free graphs states that with high probability such graphs are bipartite. Our first main result refines this theorem by investigating the structure of the ’few’ triangle-free graphs which are not bipartite. We prove that with high probability these graphs are bipartite up to a few vertices. Similar results hold if...
متن کاملoptimal orientations of subgraphs of complete bipartite graphs
for a graph g, let d(g) be the set of all strong orientations of g. the orientationnumber of g is min {d(d) |d belongs to d(g)}, where d(d) denotes the diameterof the digraph d. in this paper, we determine the orientation number for some subgraphs of complete bipartite graphs.
متن کاملConvex (anti)median Subgraphs of Graphs
The distance DG(v) of a vertex v in an undirected graph G is the sum of the distances between v and all other vertices of G. The set of vertices in G with maximum (minimum) distance is the antimedian (median) set of a graph G. In this note we prove that for every connected graph G there exists a graph H such that G is a convex subgraph of H and V (G) is the antimedian set of H . A similar const...
متن کاملComplete subgraphs in multipartite graphs
Turán’s Theorem states that every graphG of edge density ‖G‖/ (|G| 2 ) > k−2 k−1 contains a complete graph K and describes the unique extremal graphs. We give a similar Theorem for `-partite graphs. For large `, we find the minimal edge density d` , such that every `-partite graph whose parts have pairwise edge density greater than d` contains a K . It turns out that d` = k−2 k−1 for large enou...
متن کاملComplete Subgraphs of Chromatic Graphs and Hypergraphs
In this note we consider k-chromatic graphs with given colour k r-graphs have vertex sets u C i , and no r-tuple (i .e. edge o f 1 the r-graph) has two vertices in the same colour class C i .
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1981
ISSN: 0012-365X
DOI: 10.1016/0012-365x(81)90019-4