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Hajisharifi, Nasser, Tehranian, Abolfazl. (1395). A new construction for vertex decomposable graphs. , 5(3), 33-38. doi: 10.22108/toc.2016.13316
Nasser Hajisharifi; Abolfazl Tehranian. "A new construction for vertex decomposable graphs". , 5, 3, 1395, 33-38. doi: 10.22108/toc.2016.13316
Hajisharifi, Nasser, Tehranian, Abolfazl. (1395). 'A new construction for vertex decomposable graphs', , 5(3), pp. 33-38. doi: 10.22108/toc.2016.13316
Hajisharifi, Nasser, Tehranian, Abolfazl. A new construction for vertex decomposable graphs. , 1395; 5(3): 33-38. doi: 10.22108/toc.2016.13316

A new construction for vertex decomposable graphs

Transactions on Combinatorics
مقاله 57، دوره 5، شماره 3، آذر 2016، صفحه 33-38    اصل مقاله (216.85 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2016.13316
نویسندگان
Nasser Hajisharifi* 1؛ Abolfazl Tehranian2
1Department of Mathematics, Science and Research branch, Islamic Azad University, Tehran, Iran
2Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
چکیده
Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $S \subseteq V(G)$. Adding a whisker to $G$ at $x$ means adding a new vertex $y$ and edge $xy$ to $G$ where $x \in V(G)$. The graph $G\cup W(S)$ is obtained from $G$ by adding a whisker to every vertex of $S$. We prove that if $G\setminus S$ is either a graph with no chordless cycle of length other than $3$ or $5$, chordal graph or $C_5$, then $G \cup W(S)$ is a vertex decomposable graph.
کلیدواژه‌ها
vertex decomposable؛ shellabel؛ Cohen-Macaulay
مراجع
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[5] C. A. Francisco and A. Van Tuyl, Sequentially Cohen-Macaulay edge ideals, Proc. Amer. Math. Soc., 135 no. 8 (2007) 2327–2337.

[6] J. Herzog and T. Hibi, Monomial Ideals, Graduate Texts in Mathematics, 260, Springer-Verlag London, Ltd., London, 2011.

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[8] R. Woodroofe, vertex decomposable graphs and obstructions to shellability, Proc. Amer. Math. Soc., 137 no. 10 (2009) 3235–3246.

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