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\newcommand{\gem}{\mathrm{Gem}} % gem graph

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%Write your title here: 
\noindent{\bf\Large The structure of graphs excluding $\gem$ and $\hat{K_4}$ as induced minors}

%List the authors as follows (you may underline the speaker, or just
%name the speaker, and mention your co-authors at the end, up to you):  
\noindent Jarosław Błasiok -- {\small School of Engineering and Applied Sciences, 
Harvard University, United States}

\noindent Marcin Kamiński -- {\small Institute of Computer Science,
University of Warsaw, Poland}

\noindent  \underline{Jean-Florent Raymond} -- {\small Institute of Computer Science,
University of Warsaw, Poland and LIRMM -- Université de Montpellier}

\noindent Théophile Trunck -- {\small LIP, ÉNS de Lyon}


\vspace{2ex}

\noindent{\bf Abstract:} %Here write your abstract

A graph $H$ is an \emph{induced minor} of a graph $G$ it it
can be obtained by contracting an induced subgraph of $G$. When $H$ is
not an induced minor of $G$, then $G$ is said to be \emph{$H$-induced minor-free}.
%
No decomposition theorem of $H$-induced minor-free graphs is known in the general case, unlike $H$-minor-free graphs.

We give two decomposition theorems corresponding to the cases $H=\gem$ and $H = \hat{K_4}$, where $\gem$ can be constructed by adding a dominating vertex to $P_4$ and $\hat{K_4}$ by adding a vertex of degree 2 to $K_4$.
Our motivation for the choice of these two graphs was a study of the well-quasi-ordered graph classes excluding one graph as induced minors.


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