منابع مشابه
On nowhere dense graphs
A set A of vertices of a graph G is called d-scattered in G if no two d-neighborhoods of (distinct) vertices of A intersect. In other words, A is d-scattered if no two distinct vertices of A have distance at most 2d. This notion was isolated in the context of finite model theory by Gurevich and recently it played a prominent role in the study of homomorphism preservation theorems for special cl...
متن کاملFirst order properties on nowhere dense structures
A set A of vertices of a graph G is called d-scattered in G if no two d-neighborhoods of (distinct) vertices of A intersect. In other words, A is d-scattered if no two distinct vertices of A have distance at most 2d. This notion was isolated in the context of finite model theory by Gurevich and recently it played a prominent role in the study of homomorphism preservation theorems for special cl...
متن کاملReconfiguration on nowhere dense graph classes
In the token jumping problem for a vertex subset problem Q on graphs we are given a graph G and two feasible solutions Ss, St ⊆ V (G) of Q with |Ss| = |St|, and imagine that a token is placed on each vertex of Ss. The problem is to determine whether there exists a sequence S1, . . . , Sn of feasible solutions, where S1 = Ss, Sn = St and each Si+1 results from Si, 1 ≤ i < n, by moving exactly on...
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Motivated by structural decompositions and other asymptotic properties of graphs we define the notions in the title and show the wide spectrum of examples of nowhere dense graphs. This has several algorithmic consequences and it generalizes and improves earlier results.
متن کاملNowhere 0 mod p dominating sets in multigraphs
Let G be a graph with integral edge weights. A function d : V (G) → Zp is called a nowhere 0 mod p domination function if each v ∈ V satisfies ( d(v) + ∑ u∈N(v) w(u, v)d(u) ) 6= 0 mod p, where w(u, v) denotes the weight of the edge (u, v) and N(v) is the neighborhood of v. The subset of vertices with d(v) 6= 0 is called a nowhere 0 mod p dominating set. It is known that every graph has a nowher...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1980
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1980-0548097-x