A characterization of halved cubes
نویسندگان
چکیده
The vertex set of a halved cube Qd consists of a bipartition vertex set of a cube Qd and two vertices are adjacent if they have a common neighbour in the cube. Let d ≥ 5. Then it is proved that Qd is the only connected, ( d 2 ) -regular graph on 2d−1 vertices in which every edge lies in two d-cliques and two d-cliques do not intersect in a vertex.
منابع مشابه
Recognition of the ` 1 - graphs withComplexity O ( nm ) , or Football in aHypercubeM
We ll in the details of the algorithm sketched in Sh] and determine its complexity. As a part of this main algorithm, we also describe an algorithm which recognizes graphs which are isometric subgraphs of halved cubes. We discuss possible further applications of the same ideas and give a nice example of a non`1-graph allowing a highly isometric embedding into a halved cube.
متن کاملRock physics characterization of shale reservoirs: a case study
Unconventional resources are typically very complex to model, and the production from this type of reservoirs is influenced by such complexity in their microstructure. This microstructure complexity is normally reflected in their geophysical response, and makes them more difficult to interpret. Rock physics play an important role to resolve such complexity by integrating different subsurface di...
متن کاملOn density of subgraphs of halved cubes
Let S be a family of subsets of a set X of cardinality m and VC-dim(S) be the Vapnik-Chervonenkis dimension of S. Haussler, Littlestone, and Warmuth (Inf. Comput., 1994) proved that if G1(S) = (V,E) is the subgraph of the hypercube Qm induced by S (called the 1-inclusion graph of S), then |E| |V | ≤ VC-dim(S). Haussler (J. Combin. Th. A, 1995) presented an elegant proof of this inequality using...
متن کاملLOCALLY TRIANGULAR GRAPHS AND NORMAL QUOTIENTS OF THE n-CUBE
For an integer n > 2, the triangular graph has vertex set the 2-subsets of {1, . . . , n} and edge set the pairs of 2-subsets intersecting at one point. Such graphs are known to be halved graphs of bipartite rectagraphs, which are connected triangle-free graphs in which every 2-path lies in a unique quadrangle. We refine this result and provide a characterisation of connected locally triangular...
متن کاملA characterization of planar partial cubes
Partial cubes have been extensively investigated as well as planar graphs. In this note we introduce an additional topological kind of condition to the Chepoi’s expansion procedure that characterizes planar partial cubes. As a consequence we obtain a characterization of some other planar subclasses of partial cubes.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Ars Comb.
دوره 48 شماره
صفحات -
تاریخ انتشار 1998