In this article we study the monochromatic cycle partition problem for non-complete graphs. We consider graphs with a given independence number (G) = . Generalizing a classical conjecture of Erd" os, GyΓ‘rfΓ‘s and Pyber, we conjecture that if we r-color the edges of a graph G with (G) = , then the ver
β¦ LIBER β¦
Vertex partitions ofr-edge-colored graphs
β Scribed by Ze-min Jin; Xue-liang Li
- Book ID
- 107500832
- Publisher
- SP Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
- Year
- 2008
- Tongue
- English
- Weight
- 145 KB
- Volume
- 23
- Category
- Article
- ISSN
- 1005-1031
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## Abstract A __kβtree__ is a chordal graph with no (__k__β+β2)βclique. An ββ__treeβpartition__ of a graph __G__ is a vertex partition of __G__ into βbags,β such that contracting each bag to a single vertex gives an ββtree (after deleting loops and replacing parallel edges by a single edge). We pro