Geodesic
On potentially $K_5-H$-graphic sequences
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 173-182.

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Let $K_m-H$ be the graph obtained from $K_m$ by removing the edges set $E(H)$ of $H$ where $H$ is a subgraph of $K_m$. In this paper, we characterize the potentially $K_5-P_4$ and $K_5-Y_4$-graphic sequences where $Y_4$ is a tree on 5 vertices and 3 leaves.
Classification : 05C07, 05C35
Keywords: graph; degree sequence; potentially $K_5-H$-graphic sequence 
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Hu, Lili; Lai, Chunhui; Wang, Ping. On potentially $K_5-H$-graphic sequences. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 173-182. http://geodesic.mathdoc.fr/item/CMJ_2009__59_1_a11/