The strong isometric dimension of finite reflexive graphs
نویسندگان
چکیده
The strong isometric dimension of a reflexive graph is related to its injective hull: both deal with embedding reflexive graphs in the strong product of paths. We give several upper and lower bounds for the strong isometric dimension of general graphs; the exact strong isometric dimension for cycles and hypercubes; and the isometric dimension for trees is found to within a factor of two.
منابع مشابه
The existence totally reflexive covers
Let $R$ be a commutative Noetherian ring. We prove that over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$varphi:C rightarrow M$ such that $C$ is finitely generated and the projective dimension of $Kervarphi$ is finite and $varphi$ is surjective.
متن کاملOn induced and isometric embeddings of graphs into the strong product of paths
The strong isometric dimension and the adjacent isometric dimension of graphs are compared. The concepts are equivalent for graphs of diameter two in which case the problem of determining these dimensions can be reduced to a covering problem with complete bipartite graphs. Using this approach several exact strong and adjacent dimensions are computed (for instance of the Petersen graph) and a po...
متن کاملStrong Isometric Dimension, Biclique Coverings, and Sperner's Theorem
The strong isometric dimension of a graphG is the least number k such that G isometrically embeds into the strong product of k paths. Using Sperner’s Theorem, the strong isometric dimension of the Hamming graphs K2 Kn is determined.
متن کاملThe Strong Isometric Dimension of Graphs of Diameter Two
The strong isometric dimension idim(G) of a graph G is the least number k such that G can be isometrically embedded into the strong product of k paths. The problem of determining idim(G) for graphs of diameter two is reduced to a covering problem of the complement of G with complete bipartite graphs. As an example it is shown that idim(P ) = 5, where P is the Petersen graph.
متن کاملInto isometries that preserve finite dimensional structure of the range
In this paper we study linear into isometries of non-reflexive spaces (embeddings) that preserve finite dimensional structure of the range space. We consider this for various aspects of the finite dimensional structure, covering the recent notion of an almost isometric ideals introduced by Abrahamsen et.al., the well studied notions of a M -ideal and that of an ideal. We show that if a separabl...
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:
- Discussiones Mathematicae Graph Theory
دوره 20 شماره
صفحات -
تاریخ انتشار 2000