TY - JOUR
T1 - Tree-width, path-width, and cutwidth
AU - Korach, Ephraim
AU - Solel, Nir
N1 - Funding Information:
Correspondence to: Dr. E. Korach, Ben-Gurion University of the Nev, Beer-Sheva 84105, Israel * This research was partially supported by Technion V.P.R. Fund - Coleman Cohen Research Fund. ** First author’s current address: Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel. *** Second author’s current address: National Semiconducter Design Center, Herzelia, Israel.
PY - 1993/5/6
Y1 - 1993/5/6
N2 - Let tw(G), pw(G), c(G), Δ(G) denote, respectively, the tree-width, path-width, cutwidth and the maximum degree of a graph G on n vertices. It is known that c(G≥tw(G). We prove that c(G)=O(tw(G)·Δ(G)·log n), and if ({Xi: i∈I}, T=(I,A)) is a tree decomposition of G with tree-width≤k then c(G)≤(k+1)·Δ(G)·c(T). In case that a tree decomposition is given, or that the tree-width is bounded by a constant, efficient algorithms for finding a numbering with cutwidth within the upper bounds are implicit in the proofs. We obtain the above results by showing that pw(G)=O(log n·tw(G)), and pw(G)≤(k+1)·c(T).
AB - Let tw(G), pw(G), c(G), Δ(G) denote, respectively, the tree-width, path-width, cutwidth and the maximum degree of a graph G on n vertices. It is known that c(G≥tw(G). We prove that c(G)=O(tw(G)·Δ(G)·log n), and if ({Xi: i∈I}, T=(I,A)) is a tree decomposition of G with tree-width≤k then c(G)≤(k+1)·Δ(G)·c(T). In case that a tree decomposition is given, or that the tree-width is bounded by a constant, efficient algorithms for finding a numbering with cutwidth within the upper bounds are implicit in the proofs. We obtain the above results by showing that pw(G)=O(log n·tw(G)), and pw(G)≤(k+1)·c(T).
UR - http://www.scopus.com/inward/record.url?scp=38249003809&partnerID=8YFLogxK
U2 - 10.1016/0166-218X(93)90171-J
DO - 10.1016/0166-218X(93)90171-J
M3 - Article
AN - SCOPUS:38249003809
SN - 0166-218X
VL - 43
SP - 97
EP - 101
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
IS - 1
ER -