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» On Planar Quasi-Parity Graphs
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EJC
2007
15 years 6 months ago
Chords of longest circuits in locally planar graphs
It was conjectured by Thomassen ([B. Alspach, C. Godsil, Cycle in graphs, Ann. Discrete Math. 27 (1985)], p. 466) that every longest circuit of a 3-connected graph must have a cho...
Ken-ichi Kawarabayashi, Jianbing Niu, Cun-Quan Zha...
DM
1998
83views more  DM 1998»
15 years 5 months ago
The basis number of the powers of the complete graph
A basis of the cycle space C(G) of a graph G is h-fold if each edge of G occurs in at most h cycles of the basis. The basis number b(G) of G is the least integer h such that C(G) ...
Salar Y. Alsardary, Jerzy Wojciechowski
DAM
2008
131views more  DAM 2008»
15 years 6 months ago
Partition into cliques for cubic graphs: Planar case, complexity and approximation
Given a graph G = (V, E) and a positive integer k, the PARTITION INTO CLIQUES (PIC) decision problem consists of deciding whether there exists a partition of V into k disjoint sub...
Márcia R. Cerioli, L. Faria, T. O. Ferreira...
ISAAC
2005
Springer
131views Algorithms» more  ISAAC 2005»
15 years 11 months ago
Orthogonal Drawings of Series-Parallel Graphs with Minimum Bends
In an orthogonal drawing of a planar graph G, each vertex is drawn as a point, each edge is drawn as a sequence of alternate horizontal and vertical line segments, and any two edge...
Xiao Zhou, Takao Nishizeki
CORR
2000
Springer
81views Education» more  CORR 2000»
15 years 6 months ago
Safe cooperative robot dynamics on graphs
This paper initiates the use of vector fields to design, optimize, and implement reactive schedules for safe cooperative robot patterns on planar graphs. We consider Automated Gui...
Robert Ghrist, Daniel E. Koditschek