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A study on partitioning planar graphs without 4-cycles and 5-cycles
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 박보람 | - |
| dc.contributor.author | 서형준 | - |
| dc.date.accessioned | 2022-11-29T03:01:11Z | - |
| dc.date.available | 2022-11-29T03:01:11Z | - |
| dc.date.issued | 2022-02 | - |
| dc.identifier.other | 31433 | - |
| dc.identifier.uri | https://dspace.ajou.ac.kr/handle/2018.oak/20858 | - |
| dc.description | 학위논문(석사)--아주대학교 일반대학원 :수학과,2022. 2 | - |
| dc.description.tableofcontents | 1 Introduction 1 1.1 Definitions 1 1.2 History of Steinberg's Conjecture 2 1.3 The topic of this thesis and the main result 4 2 Preliminaries 5 2.1 Method for proofs 5 2.2 Definitions and basic lemmas in this thesis 5 3 Proof of Theorem 15 8 3.1 Reducible configurations 8 3.2 Discharging rules 14 국문초록 21 | - |
| dc.language.iso | kor | - |
| dc.publisher | The Graduate School, Ajou University | - |
| dc.rights | 아주대학교 논문은 저작권에 의해 보호받습니다. | - |
| dc.title | A study on partitioning planar graphs without 4-cycles and 5-cycles | - |
| dc.type | Thesis | - |
| dc.contributor.affiliation | 아주대학교 일반대학원 | - |
| dc.contributor.alternativeName | HyungJun Seo | - |
| dc.contributor.department | 일반대학원 수학과 | - |
| dc.date.awarded | 2022. 2 | - |
| dc.description.degree | Master | - |
| dc.identifier.localId | 1245040 | - |
| dc.identifier.uci | I804:41038-000000031433 | - |
| dc.identifier.url | https://dcoll.ajou.ac.kr/dcollection/common/orgView/000000031433 | - |
| dc.subject.keyword | Cycle length restriction | - |
| dc.subject.keyword | Improper coloring | - |
| dc.subject.keyword | Planar graphs | - |
| dc.subject.keyword | Steinberg’s conjecture | - |
| dc.subject.keyword | Vertex partition. | - |
| dc.description.alternativeAbstract | 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. | - |
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- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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