From 5638b976f2fd1c50670d2ef7e6e6832fdc2a2dd8 Mon Sep 17 00:00:00 2001 From: Franciszek Malinka Date: Thu, 21 Apr 2022 01:28:40 +0200 Subject: Removed a todo --- lic_malinka.pdf | Bin 386727 -> 386018 bytes lic_malinka.tex | 5 ++--- 2 files changed, 2 insertions(+), 3 deletions(-) diff --git a/lic_malinka.pdf b/lic_malinka.pdf index 2bd9a82..b5e7ed2 100644 Binary files a/lic_malinka.pdf and b/lic_malinka.pdf differ diff --git a/lic_malinka.tex b/lic_malinka.tex index e1a45b3..af116cd 100644 --- a/lic_malinka.tex +++ b/lic_malinka.tex @@ -582,9 +582,8 @@ Take any graphs $(A, \alpha), (B, \beta), (C,\gamma)$ such that $A$ embeds into $B$ and $C$. Let $D$ be the amalgamation of $B$ and $C$ over $A$ as in the proof for the plain graphs. We will define the automorphism - $\delta\in\Aut(D)$ so it extends $\beta$ and $\gamma$. (TODO: chyba nie - tylko extends ale coś więcej: wiem o co chodzi, ale nie wiem jak to - napisać) We let $\delta_{\upharpoonright X} = \id_X$ for $X\in \{A, + $\delta\in\Aut(D)$ so it extends $\beta$ and $\gamma$. + We let $\delta_{\upharpoonright X} = \id_X$ for $X\in \{A, B\setminus A, C\setminus B\}$. Let's check the definition is correct. In order to do that, we have to show that for any $u, v\in D\quad(uE_Dv\leftrightarrow \delta(u)E_D\delta(v))$. We have two cases: -- cgit v1.2.3