TY - JOUR
T1 - On planar graphs with large tree-width and small grid minors.
AU - Grigoriev, A.
AU - Marchal, L.
AU - Usotskaya, N.
PY - 2009/1/1
Y1 - 2009/1/1
N2 - Given a simple planar graph with tree-width w and side size of the largest square grid minor g, it is known that g?w?5g-1g?w?5g-1. Thus, the side size of the largest grid minor is a constant approximation for the tree-width in planar graphs. In this work we analyze the lower bounds of this approximation. In particular, we present a class of planar graphs with ?3g/2?-1?w?3g/2??3g/2?-1?w??3g/2?. We conjecture that in the worst case w=2g+o(g)w=2g+o(g). For this conjecture we have two candidate classes of planar graphs.
AB - Given a simple planar graph with tree-width w and side size of the largest square grid minor g, it is known that g?w?5g-1g?w?5g-1. Thus, the side size of the largest grid minor is a constant approximation for the tree-width in planar graphs. In this work we analyze the lower bounds of this approximation. In particular, we present a class of planar graphs with ?3g/2?-1?w?3g/2??3g/2?-1?w??3g/2?. We conjecture that in the worst case w=2g+o(g)w=2g+o(g). For this conjecture we have two candidate classes of planar graphs.
U2 - 10.1016/j.endm.2009.02.006
DO - 10.1016/j.endm.2009.02.006
M3 - Article
SN - 1571-0653
VL - 32
SP - 35
EP - 42
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -