论文信息 - Two-Page Book Embeddings of 4-Planar Graphs

Two-Page Book Embeddings of 4-Planar Graphs

Back in the eighties, Heath [Algorithms for embedding graphs in books. PhD thesis, University of North Carolina, Chapel Hill, 1985] showed that every 3-planar graph is subhamiltonian and asked whether this result can be extended to a class of graphs of degree greater than three. In this paper we affirmatively answer this question for the class of 4-planar graphs. Our contribution consists of two algorithms: The first one is limited to triconnected graphs, but runs in linear time and uses existing methods for computing hamiltonian cycles in planar graphs. The second one, which solves the general case of the problem, is a quadratic-time algorithm based on the book embedding viewpoint of the problem.

Michael A. Bekos | Martin Gronemann | Chrysanthi N. Raftopoulou | Martin Gronemann | M. Bekos

[1] Arnold L. Rosenberg,et al. Embedding graphs in books: a layout problem with applications to VLSI design , 1985 .

[2] Guido Helden. Each maximal planar graph with exactly two separating triangles is Hamiltonian , 2007, Discret. Appl. Math..

[3] Chiuyuan Chen. Any Maximal Planar Graph with Only One Separating Triangle is Hamiltonian , 2003, J. Comb. Optim..

[4] W. T. Tutte. A THEOREM ON PLANAR GRAPHS , 1956 .

[5] H. Whitney. A Theorem on Graphs , 1931 .

[6] Mihalis Yannakais,et al. Embedding planar graphs in four pages , 1989, STOC 1989.

[7] Norishige Chiba,et al. The Hamiltonian Cycle Problem is Linear-Time Solvable for 4-Connected Planar Graphs , 1989, J. Algorithms.

[8] Michael A. Bekos,et al. Two-Page Book Embeddings of 4-Planar Graphs , 2014, STACS.

[9] Paul C. Kainen,et al. The book thickness of a graph , 1979, J. Comb. Theory, Ser. B.

[10] Lenwood S. Heath. Embedding Planar Graphs in Seven Pages , 1984, FOCS.

[11] Mihalis Yannakakis,et al. Embedding Planar Graphs in Four Pages , 1989, J. Comput. Syst. Sci..

[12] Lenwood S. Heath. Algorithms for embedding graphs in books (planar, vlsi, fault-tolerant, hamiltonian cycle, trivalent) , 1985 .

[13] Paul C. Kainen,et al. Extension of a theorem of Whitney , 2007, Appl. Math. Lett..

[14] David R. Wood,et al. On Linear Layouts of Graphs , 2004, Discret. Math. Theor. Comput. Sci..

[15] Daniel P. Sanders. On paths in planar graphs , 1997, J. Graph Theory.