Pancyclicity of 4-Connected $$\{K_{1,3},Z_8\}$$ { K 1 , 3 , Z 8 } -Free Graphs
| Autor: | Hong-Jian Lai, Ju Zhou, Mingquan Zhan, Taoye Zhang |
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| Rok vydání: | 2018 |
| Předmět: |
Vertex (graph theory)
0211 other engineering and technologies 021107 urban & regional planning 0102 computer and information sciences 02 engineering and technology Free graph 01 natural sciences Graph Theoretical Computer Science law.invention Combinatorics 010201 computation theory & mathematics law Petersen graph Line graph Discrete Mathematics and Combinatorics Mathematics |
| Zdroj: | Graphs and Combinatorics. 35:67-89 |
| ISSN: | 1435-5914 0911-0119 |
| DOI: | 10.1007/s00373-018-1987-4 |
| Popis: | A graph G is said to be pancyclic if G contains cycles of lengths from 3 to |V(G)|. For a positive integer i, we use $$Z_i$$ to denote the graph obtained by identifying an endpoint of the path $$P_{i+1}$$ with a vertex of a triangle. In this paper, we show that every 4-connected claw-free $$Z_8$$ -free graph is either pancyclic or is the line graph of the Petersen graph. This implies that every 4-connected claw-free $$Z_6$$ -free graph is pancyclic, and every 5-connected claw-free $$Z_8$$ -free graph is pancyclic. |
| Databáze: | OpenAIRE |
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