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Quasi-line graph とは
谷口 哲至
Let $\small{H^{(m) } }$ be a Hoffman graph satisfying the following conditions:
(i) the subgraph induced by all slim vertices is complete graph with $\small{m}$ vertices,
(ii) $\small{H^{(m) } }$ has exactly two fat vertices,
(iii) every fat vertex is adjacent to all slim vertices.
Let $\small \mathscr{H}_m:=\{[H^{(i)}]\mid i=1,2,\ldots,m\}$.
Note $\small H_2$, $\small H_{14}\in\mathscr{H}_{\infty}$.
Then all quasi-line graph are slim $\small \mathscr{H}_\infty$-line graph.
参考文献：
Chudnovsky, Maria(1-PRIN); Ovetsky, Alexandra(1-PRIN)
Coloring quasi-line graphs. (English summary)
J. Graph Theory 54 (2007), no. 1, 41--50.
Coloring quasi-line graphs. (English summary)
J. Graph Theory 54 (2007), no. 1, 41--50.
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初
記録をとるのにええかも
$H=\biguplus_{i=1}^nH^i, \text{ where } H^i\in\mathscr{H}\text{ for }\forall i$
けっこういろいろ書ける・・・
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