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

VL - 32

SP - 35

EP - 42

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

ER -