I,F-partitions of sparse graphs
A stark-coloring is a proper k-coloring where the union of two color classes induces a star forest. While every planar graph is 4-colorable, not every planar graph is star 4-colorable. One method to produce a star 4-coloring is to partition the vertex set into a 2-independent set and a forest; such...
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| Veröffentlicht in: | European journal of combinatorics 2016-10, Vol.57, p.1-12 |
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| container_title | European journal of combinatorics |
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| creator | Brandt, Axel Ferrara, Michael Kumbhat, Mohit Loeb, Sarah Stolee, Derrick Yancey, Matthew |
| description | A stark-coloring is a proper k-coloring where the union of two color classes induces a star forest. While every planar graph is 4-colorable, not every planar graph is star 4-colorable. One method to produce a star 4-coloring is to partition the vertex set into a 2-independent set and a forest; such a partition is called an I,F-partition. We use a combination of potential functions and discharging to prove that every graph with maximum average degree less than 52 has an I,F-partition, which is sharp and answers a question of Cranston and West (0000). This result implies that planar graphs of girth at least 10 are star 4-colorable, improving upon previous results of Bu et al. (2009). |
| doi_str_mv | 10.1016/j.ejc.2016.03.003 |
| format | Article |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Color Combinatorial analysis Forests Graphs Mathematical analysis Partitions Stars Unions |
| title | I,F-partitions of sparse graphs |
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