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A study on partitioning planar graphs without 4-cycles and 5-cycles
- Author(s)
- 서형준
- Alternative Author(s)
- HyungJun Seo
- Advisor
- 박보람
- Department
- 일반대학원 수학과
- Publisher
- The Graduate School, Ajou University
- Publication Year
- 2022-02
- Language
- kor
- Keyword
- Cycle length restriction; Improper coloring; Planar graphs; Steinberg’s conjecture; Vertex partition.
- Alternative Abstract
- In 1976, Steinberg conjectured that planar graphs without 4-cycles and 5-cycles are 3-colorable. This conjecture attracted numerous researchers for about 40 years until it was disproved by Cohen-Addad et al. in 2017. How- ever, coloring planar graphs with restrictions on cycle lengths is still an active area of research, and the interest in this particular graph class remains. Recently, Cho, Choi, Park (2021) showed that for a planar graph G without 4-cycles and 5-cycles, V (G) is partitioned into two sets A and B such that G[A] and G[B] are forests with maximum degree three and four, respectively. In this thesis, we show that for a planar graph G without 4- cycles and 5-cycles, V (G) is partitioned into two sets A and B such that G[A] is a linear forest and G[B] has maximum degree at most 8.
- Fulltext
- Appears in Collections:
- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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