\(\mathsf{K}_{4}\)-free

Autor

Enric Cosme Llópez

Publicat

April 1, 2018

K4.tex
\documentclass[10pt, a4paper]{paper}
\usepackage[english]{babel}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{enumerate,color,xfrac}
\usepackage{mathpartir}
\usepackage{xargs}

\usepackage{tikz}
\usetikzlibrary{mindmap,backgrounds}
\usetikzlibrary{matrix,chains,scopes,arrows,fit}
\usetikzlibrary{positioning,calc,shapes}
\usetikzlibrary{automata} 
\usetikzlibrary{arrows}
\usetikzlibrary{through}

    %%%% ARROWS
\tikzstyle{arc} =[thick,->,>=latex]
\tikzstyle{arcp}=[thick,-,>=latex]

    %%%% NODES
\newcommand\initst[1]{\draw[arc] ($ (#1) + (-0.6,0) $) to (#1)}
\newcommand\fnst[1]{\draw[arc] (#1) to ($ (#1) + (0.6,0) $)}
\tikzstyle{vert}=[thick,draw,circle,fill=gray!20,inner sep=1.5]
\tikzstyle{every node}=[font=\footnotesize]
\newcommand\vertex[3][vert]{\node[#1] (#2) at (#3) {}}

    %%%% COLORS
\definecolor{Salmon}{RGB}{250,128,114}
\definecolor{Crimson}{RGB}{220,20,60}
\definecolor{DarkOrange}{RGB}{255,140,0}
\definecolor{Khaki}{RGB}{240,230,140}
\definecolor{GreenYellow}{RGB}{173,255,47}
\definecolor{MediumSeaGreen}{RGB}{60,179,113}
\definecolor{OliveDrab}{RGB}{107,142,35}
\definecolor{LightSeaGreen}{RGB}{32,178,170}
\definecolor{Aquamarine}{RGB}{127,255,212}
\definecolor{SteelBlue}{RGB}{70,130,180}
\definecolor{Navy}{RGB}{0,0,128}
\definecolor{Purple}{RGB}{128,0,128}
\definecolor{Orchid}{RGB}{218,112,214}
\definecolor{Brown}{RGB}{165,42,42}
\definecolor{Chocolate}{RGB}{210,105,30}
\definecolor{SandyBrown}{RGB}{244,164,96}
\definecolor{ForestGreen}{RGB}{34,139,34}
\definecolor{Gold}{RGB}{255,215,0}
\definecolor{Yellow}{RGB}{255,255,0}    
    
    %%%% ENVIRONMENTS
\tikzstyle{J}=[fill=Yellow, thick, even odd rule]
\tikzstyle{H}=[fill=MediumSeaGreen, thick, even odd rule]
\tikzstyle{B}=[fill=SteelBlue, thick, even odd rule]

    %%%%TRANSPARENT
\tikzstyle{Jtransparent}=[J,    fill opacity=.3]
\tikzstyle{Htransparent}=[H,    fill opacity=.3]
\tikzstyle{Btransparent}=[B,    draw=SteelBlue, fill opacity=.3, draw opacity=.4]
    
    %%%%BAGS
\newcommandx*\Hbag[4][3=0, 4=H, usedefault]
            {\filldraw[#4,  shift={(#1,#2)}, rotate=#3] 
            ellipse (\Alt cm and \Dist cm);}
\newcommandx*\Jbag[4][3=0, 4=J, usedefault]
            {\filldraw[#4,  shift={(#1,#2)}, rotate=#3]
            (0,0)   ++ (0,\pinC)    ++ (\pinAngleRight:\pinB)
            arc[at={(0,0)},         start angle=\pinAngleRight,             
            delta angle=360-2*\pinAngle,    radius=\pinB]               
            -- (0,0) -- cycle;}

\begin{document}
\thispagestyle{empty}
\begin{center}
\begin{tikzpicture}[scale=1]
      \pgfmathsetmacro{\pinB}{.05mm};
      \pgfmathsetmacro{\pinC}{.1mm};
      \pgfmathsetmacro{\pinAngle}{acos(\pinB/\pinC)};
      \pgfmathsetmacro{\pinAngleRight}{270+\pinAngle};      
      \pgfmathsetmacro{\Alt}{.5};
      \pgfmathsetmacro{\Dist}{.2};                  
      \Hbag{0}{1};
      \Hbag{-.93}{.78}[30][Htransparent];   
      \Hbag{-.35}{.5}[110][Htransparent];
      \Hbag{.9}{.7}[135][Htransparent];
      \Jbag{-.5}{1.15}[12];                         %0
      \Jbag{.5}{1.15}[-12];                         %1
      \Jbag{1.25}{.4}[-40][Jtransparent];           %2
      \Jbag{-1.4}{.55}[36][Jtransparent];           %3
      \Jbag{-.25}{-0.02}[60][Jtransparent];         %4 
      \node (0) at (-.5,1) [vert] {};
      \node (1) at (.5,1)  [vert] {};
      \vertex 2 {1.23,.38};
      \vertex 3 {-1.35,.55};
      \vertex 4 {-.22,0};
      \node (i) at (0,-.7) [vert] {};
      \initst i; \fnst i;
      \draw[arcp, dashed] (i) to node [] {} (3); 
      \draw[arcp, dashed] (i) to node [] {} (4); 
      \draw[arcp, dashed] (i) to node [] {} (2);
      \draw [Btransparent] plot [smooth cycle] coordinates 
      { (-.7,1.2) (-1.4,1.3) (-1.8,1) (-1.6,-.1) (0,-.7) (-.2,.75)};
      \draw [Btransparent] plot [smooth cycle] coordinates 
      { (.7,1.2) (1.4,1.3) (1.8,1) (1.6,-.1) (0,-.7) (.2,.75)};
      \node () at (0,-.7) [vert] {$\iota$};
      \node () at (-.5,1) [vert] {$x$};
      \node () at (.5,1) [vert] {$y$};
      \node () at (-1.4,0) [] {$\scriptstyle a$};
      \node () at (1.4,0) [] {$\scriptstyle c$};
      \node () at (-.85,1.5) [] {$\scriptstyle \alpha$};
      \node () at (.85,1.5) [] {$\scriptstyle \gamma$};
      \node () at (0,1) [] {$\scriptstyle b$};
\end{tikzpicture}
\end{center}
\end{document}