منابع مشابه
Separation dimension of bounded degree graphs
The separation dimension of a graph G is the smallest natural number k for which the vertices of G can be embedded in Rk such that any pair of disjoint edges in G can be separated by a hyperplane normal to one of the axes. Equivalently, it is the smallest possible cardinality of a family F of total orders of the vertices of G such that for any two disjoint edges of G, there exists at least one ...
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A family F of permutations of the vertices of a hypergraph H is called pairwise suitable for H if, for every pair of disjoint edges in H , there exists a permutation in F in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for H is called the separation dimension of H and is denoted by π(H). Equivalently, π(H) is the smalle...
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We show that the intersection dimension of graphs with respect to several hereditary graph classes can be bounded as a function of the maximum degree. As an interesting special case, we show that the circular dimension of a graph with maximum degree ∆ is at most O(∆ log∆ log log∆). We also obtain bounds in terms of treewidth.
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15 صفحه اولSeparation dimension of sparse graphs
The separation dimension of a graph G is the smallest natural number k for whichthe vertices of G can be embedded in Rk such that any pair of disjoint edges in G canbe separated by a hyperplane normal to one of the axes. Equivalently, it is the smallestpossible cardinality of a family F of permutations of the vertices of G such that for anytwo disjoint edges of G, there exists a...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2019
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004119000525