Abstract
The vertex arboricity va(G) of a graph G is the minimum number of subsets into which the vertex set V(G) can be partitioned so that each subset induces an acyclic subgraph. The fractional version of vertex arboricity is introduced in this paper. We determine fractional vertex arboricity for several classes of graphs, e.g., complete multipartite graphs, cycles, integer distance graphs, prisms and Peterson graph.
This work is supported by Nankai University Overseas Scholar Grant, RFDP of Higher Education of China and Discovery Grant of NSERC of Canada.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chvátal, V.: Linear Programming. W. H. Freeman and Company, New York (1983)
Chartrand, G., Kronk, H.V., Wall, C.E.: The Point Arboricity of a Graph. Israel J. Math. 6, 169–175 (1968)
Goddard, W.: Acyclic Coloring of Planar Graphs. Discrete Math. 91, 91–94 (1991)
Kronk, H.V., Mitchem, J.: Critical Point-Arboritic Graphs. J. London Math. Soc. 9(2), 459–466 (1975)
Škrekovski, R.: On the Critical Point-Arboricity Graphs. J. Graph Theory 39, 50–61 (2002)
Scheinerman, E.R., Ullman, D.H.: Fractional Graph Theory. John Wiley and Sons. Inc, New York (1997)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Yu, Q., Zuo, L. (2007). Fractional Vertex Arboricity of Graphs. In: Akiyama, J., Chen, W.Y.C., Kano, M., Li, X., Yu, Q. (eds) Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol 4381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70666-3_26
Download citation
DOI: https://doi.org/10.1007/978-3-540-70666-3_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70665-6
Online ISBN: 978-3-540-70666-3
eBook Packages: Computer ScienceComputer Science (R0)