A note on 3-connected hourglass-free claw-free Hamilton-connected graphs

Xia Liu; Liming Xiong

doi:10.1016/j.disc.2022.112910

A note on 3-connected hourglass-free claw-free Hamilton-connected graphs

Xia Liu, Liming Xiong^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

An hourglass Γ₀ is the graph with degree sequence (4, 2, 2, 2, 2) and a claw is the bipartite complete graph K_1,3. In this paper, we show that (1) every 3-connected, essentially 4-connected {K_1,3,Γ₀}-free graph is Hamilton-connected, (2) every 3-connected {K_1,3,Γ₀,P₁₆}-free graph is Hamilton-connected, where (1) improves similar results of (Li et al. (2008) [11]) and hence (Broersma et al. (2001) [4]); (2) settles one conjecture posed in (Ryjáček et al. (2018) [18]).

Original language	English
Article number	112910
Journal	Discrete Mathematics
Volume	345
Issue number	8
DOIs	https://doi.org/10.1016/j.disc.2022.112910
Publication status	Published - Aug 2022

Keywords

Hamilton-connected
Hourglass-free
Line graph
SM-closure
Strongly spanning trailable

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10.1016/j.disc.2022.112910

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Liu, X., & Xiong, L. (2022). A note on 3-connected hourglass-free claw-free Hamilton-connected graphs. Discrete Mathematics, 345(8), Article 112910. https://doi.org/10.1016/j.disc.2022.112910

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title = "A note on 3-connected hourglass-free claw-free Hamilton-connected graphs",

abstract = "An hourglass Γ0 is the graph with degree sequence (4, 2, 2, 2, 2) and a claw is the bipartite complete graph K1,3. In this paper, we show that (1) every 3-connected, essentially 4-connected {K1,3,Γ0}-free graph is Hamilton-connected, (2) every 3-connected {K1,3,Γ0,P16}-free graph is Hamilton-connected, where (1) improves similar results of (Li et al. (2008) [11]) and hence (Broersma et al. (2001) [4]); (2) settles one conjecture posed in (Ryj{\'a}{\v c}ek et al. (2018) [18]).",

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author = "Xia Liu and Liming Xiong",

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AB - An hourglass Γ0 is the graph with degree sequence (4, 2, 2, 2, 2) and a claw is the bipartite complete graph K1,3. In this paper, we show that (1) every 3-connected, essentially 4-connected {K1,3,Γ0}-free graph is Hamilton-connected, (2) every 3-connected {K1,3,Γ0,P16}-free graph is Hamilton-connected, where (1) improves similar results of (Li et al. (2008) [11]) and hence (Broersma et al. (2001) [4]); (2) settles one conjecture posed in (Ryjáček et al. (2018) [18]).

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A note on 3-connected hourglass-free claw-free Hamilton-connected graphs

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Keywords

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