TY - GEN

T1 - Small grid drawings of planar graphs with balanced bipartition

AU - Zhou, Xiao

AU - Hikino, Takashi

AU - Nishizeki, Takao

N1 - Funding Information:
This work is supported in part by a Grant-in-Aid for Scientific Research (C) 19500001 from Japan Society for the Promotion of Science (JSPS).

PY - 2010

Y1 - 2010

N2 - In a grid drawing of a planar graph, every vertex is located at a grid point, and every edge is drawn as a straight-line segment without any edge-intersection. It has been known that every planar graph G of n vertices has a grid drawing on an (n-2)×(n-2) integer grid and such a drawing can be found in linear time. In this paper we show that if a planar graph G has a balanced bipartition then G has a grid drawing with small grid area. More precisely, if a separation pair bipartitions G into two edge-disjoint subgraphs G1 and G2, then G has a grid drawing on a W×H grid such that both the width W and height H are smaller than the larger number of vertices in G1 and in G2. In particular, we show that every series-parallel graph G has a grid drawing on a (2n/3)×(2n/3) grid and such a drawing can be found in linear time.

AB - In a grid drawing of a planar graph, every vertex is located at a grid point, and every edge is drawn as a straight-line segment without any edge-intersection. It has been known that every planar graph G of n vertices has a grid drawing on an (n-2)×(n-2) integer grid and such a drawing can be found in linear time. In this paper we show that if a planar graph G has a balanced bipartition then G has a grid drawing with small grid area. More precisely, if a separation pair bipartitions G into two edge-disjoint subgraphs G1 and G2, then G has a grid drawing on a W×H grid such that both the width W and height H are smaller than the larger number of vertices in G1 and in G2. In particular, we show that every series-parallel graph G has a grid drawing on a (2n/3)×(2n/3) grid and such a drawing can be found in linear time.

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U2 - 10.1007/978-3-642-11440-3_5

DO - 10.1007/978-3-642-11440-3_5

M3 - Conference contribution

AN - SCOPUS:77949603349

SN - 3642114393

SN - 9783642114397

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 47

EP - 57

BT - WALCOM

T2 - 4th International Workshop on Algorithms and Computation, WALCOM 2010

Y2 - 10 February 2010 through 12 February 2010

ER -