IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Special Section on Discrete Mathematics and Its Applications
On the Structure of Locally Outerplanar Graphs
Hung-Lung WANGChun-Yu TSENGJou-Ming CHANG
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2015 Volume E98.A Issue 6 Pages 1212-1215

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Abstract

For k ≥ 3, a convex geometric graph is called k-locally outerplanar if no path of length k intersects itself. In [D. Boutin, Convex Geometric Graphs with No Short Self-intersecting Path, Congressus Numerantium 160 (2003) 205-214], Boutin stated the results of the degeneracy for 3-locally outerplanar graphs. Later, in [D. Boutin, Structure and Properties of Locally Outerplanar Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 60 (2007) 169-180], a structural property on k-locally outerplanar graphs was proposed. These results are based on the existence of “minimal corner pairs”. In this paper, we show that a “minimal corner pair” may not exist and give a counterexample to disprove the structural property. Furthermore, we generalize the result on the degeneracy with respect to k-locally outerplanar graphs.

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© 2015 The Institute of Electronics, Information and Communication Engineers
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