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- W2015352917 abstract "We represent a graph by assigning each vertex a finite set such that vertices are adjacent if and only if the corresponding sets have at least two common elements. The 2-intersection number θ2(G) of a graph G is the minimum size of the union of sets in such a representation. We prove that the maximum order of a path that can be represented in this way using t elements is between (t2 - 19t + 4)/4 and (t2 - t + 6)/4, making θ2(Pn) asymptotic to 2√n. We also show the existence of a constant c depending on ϵ such that, for any tree T with maximum degree at most d, θ2(T) ≤ c(√n)1+ϵ. When the maximum degree is not bounded, there is an n-vertex tree T with θ2(T) > .945n2/3. © 1995 John Wiley & Sons, Inc." @default.
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- W2015352917 date "1995-07-01" @default.
- W2015352917 modified "2023-09-25" @default.
- W2015352917 title "The 2-intersection number of paths and bounded-degree trees" @default.
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- W2015352917 doi "https://doi.org/10.1002/jgt.3190190403" @default.
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