Geodesic
Degree sequences of graphs containing a cycle with prescribed length
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 2, pp. 481-487.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Let $r\ge 3$, $n\ge r$ and $\pi =(d_1,d_2,\ldots ,d_n)$ be a non-increasing sequence of nonnegative integers. If $\pi $ has a realization $G$ with vertex set $V(G)=\{v_1,v_2,\ldots ,v_n\}$ such that $d_G(v_i)=d_i$ for $i=1,2,\ldots , n$ and $v_1v_2\cdots v_rv_1$ is a cycle of length $r$ in $G$, then $\pi $ is said to be potentially $C_r''$-graphic. In this paper, we give a characterization for $\pi $ to be potentially $C_r''$-graphic.
Classification : 05C07, 05C38
Keywords: graph; degree sequence; potentially $C_r$-graphic sequence 
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     author = {Yin, Jian-Hua},
     title = {Degree sequences of graphs containing a cycle with prescribed length},
     journal = {Czechoslovak Mathematical Journal},
     pages = {481--487},
     publisher = {mathdoc},
     volume = {59},
     number = {2},
     year = {2009},
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     zbl = {1224.05107},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009__59_2_a12/}
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Yin, Jian-Hua. Degree sequences of graphs containing a cycle with prescribed length. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 2, pp. 481-487. http://geodesic.mathdoc.fr/item/CMJ_2009__59_2_a12/