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• W2003998639 abstract "A graph G is K-chordal, if it does not contain chordless cycles of length larger than k. The chordality lc of a graph G is the minimum k for which G is k-chordal. The degeneracy or the width of a graph is the maximum min-degree of any of its subgraphs. Our results are the following: (1) The problem of treewidth remains NP-complete when restricted to graphs with small maximum degree. (2) An upper bound is given for the treewidth of a graph as a function of its maximum degree and chordality. A consequence of this result is that when maximum degree and chordality are fixed constants, then there is a linear algorithm for treewidth and a polynomial algorithm for pathwidth. (3) For any constant s ⩾ 1, it is shown that any (s + 2)-chordal graph with bounded width contains an 12-separator of size O(n(s − 1)s), computable in O(n3 −(1s)) time. Our results extent the many applications of the separator theorems in [1, 32, 33] to the class of K-chordal graphs." @default.
• W2003998639 created "2016-06-24" @default.
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• W2003998639 date "1997-11-01" @default.
• W2003998639 modified "2023-10-18" @default.
• W2003998639 title "Treewidth for graphs with small chordality" @default.
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• W2003998639 doi "https://doi.org/10.1016/s0166-218x(97)00031-0" @default.
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