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Sufficient conditions for triangle-free graphs to be super-$λ'$ | ||
| Transactions on Combinatorics | ||
| مقاله 3، دوره 7، شماره 3، آذر 2018، صفحه 29-36 اصل مقاله (228.44 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2018.106623.1523 | ||
| نویسندگان | ||
| Huiwen Cheng* 1؛ Yan-Jing Li2 | ||
| 1Department of Mathematics, Zhongguancun Institute | ||
| 2Department of Mathematics, Beijing Jiaotong University, China | ||
| چکیده | ||
| An edge-cut $F$ of a connected graph $G$ is called a restricted edge-cut if $G-F$ contains no isolated vertices. The minimum cardinality of all restricted edge-cuts is called the restricted edge-connectivity $λ'(G)$ of $G$. A graph $G$ is said to be $λ'$-optimal if $λ'(G)=\xi(G)$, where $\xi(G)$ is the minimum edge-degree of $G$. A graph is said to be super-$λ'$ if every minimum restricted edge-cut isolates an edge. In this paper, first, we provide a short proof of a previous theorem about the sufficient condition for $λ'$-optimality in triangle-free graphs, which was given in [J. Yuan and A. Liu, Sufficient conditions for $λ_k$-optimality in triangle-free graphs, Discrete Math., 310 (2010) 981--987]. Second, we generalize a known result about the sufficient condition for triangle-free graphs being super-$λ'$ which was given by Shang et al. in [L. Shang and H. P. Zhang, Sufficient conditions for graphs to be $λ'$-optimal and super-$λ'$, Network}, 309 (2009) 3336--3345]. | ||
| کلیدواژه‌ها | ||
| Triangle-free؛ restricted edge-cut؛ super-$ld'$ | ||
| مراجع | ||
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