منابع مشابه
Classification of graphs based on homotopy equivalence. Homotopy equivalent graphs. Basic graphs and complexity of homotopy equivalence classes of graphs
The main concept of this classification is that graphs belonging to the same equivalence class have similar topological properties. Graphs are called homotopy equivalent if one of them can be converted to the other one by contractible transformations. A basic representative and complexity of a homotopy equivalence class are defined and investigated. Finding a basic representative within a homot...
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Recently a new homotopy theory for graphs and simplicial complexes was defined (cf. [3, 4]). The motivation for the definition came initially from a desire to find invariants for dynamic processes that could be encoded via (combinatorial) simplicial complexes. The invariants were supposed to be topological in nature, but should at the same time be sensitive to the combinatorics encoded in the c...
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The singular simplicial set Sing(X) of a space X completely captures its weak homotopy type. We introduce a category of controlled sets, yielding simplicial controlled sets, such that one can functorially produce a singular simplicial controlled set CSing(MaxCtl(X)) from a locally compact X. We then argue that this CSing(MaxCtl(X)) captures the (weak) proper homotopy type of X. Moreover, our te...
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An edge-colored graph G is k-proper connected if every pair of vertices is connected by k internally pairwise vertex-disjoint proper colored paths. The k-proper connection number of a connected graph G, denoted by pck(G), is the smallest number of colors that are needed to color the edges ofG in order tomake it k-proper connected. In this paperweprove several upper bounds for pck(G). We state s...
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Gerbes are locally connected presheaves of groupoids on a small Grothendieck site C. Gerbes are classified up to local weak equivalence by path components of a cocycle category taking values in the diagram Grp(C) of 2-groupoids consisting of all sheaves of groups, their isomorphisms and homotopies. If F is a full subpresheaf of Grp(C) then the set [∗, BF ] of morphisms in the homotopy category ...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 1990
ISSN: 0024-6093
DOI: 10.1112/blms/22.5.417