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On the critical point-arboricity graphs

✍ Scribed by Riste Škrekovski

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 155 KB
Volume: 39
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10010

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✦ Synopsis

Abstract

In this paper, we study the critical point‐arboricity graphs. We prove two lower bounds for the number of edges of k‐critical point‐arboricity graphs. A theorem of Kronk is extended by proving that the point‐arboricity of a graph G embedded on a surface S with Euler genus g = 2, 5, 6 or g ≥ 10 is at most $k =\lfloor {9 +\sqrt {1+ 24, g}\over 4}\rfloor$ with equality holding iff G contains either K~2__k__−1~ or K~2__k__−4~ + C~5~ as a subgraph. It is also proved that locally planar graphs have point‐arboricity ≤ 3 and that triangle‐free locally planar‐graphs have point‐arboricity ≤ 2. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 50–61, 2002

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