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A mathematical procedure enabling the transformation of an arbitrary tessellation of a surface into a bi-colored, complete graph is introduced. Polygons constituting the tessellation are represented by vertices of the graphs. Vertices of the graphs are connected by two kinds of links/edges, namely, by a green link, when polygons have the same number of sides, and by a red link, when the polygons have a different number of sides. This procedure gives rise to a semi-transitive, complete, bi-colored Ramsey graph. The Ramsey semi-transitive number was established as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mrow><mi>t</mi><mi>r</mi><mi>a</mi><mi>n</mi><mi>s</mi></mrow></msub><mrow><mo>(</mo><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow><mo>)</mo></mrow><mo>=</mo><mn>5</mn></mrow></semantics></math></inline-formula> Shannon entropies of the tessellation and graphs are introduced. Ramsey graphs emerging from random Voronoi and Poisson Line tessellations were investigated. The limits <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>=</mo><munder><mrow><mi>lim</mi></mrow><mrow><mi>N</mi><mo>→</mo><mo>∞</mo></mrow></munder><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><msub><mi>N</mi><mi>g</mi></msub></mrow><mrow><msub><mi>N</mi><mi>r</mi></msub></mrow></mfrac></mstyle></mrow></semantics></math></inline-formula>, where <i>N</i> is the total number of green and red seeds, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mi>g</mi></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mi>r</mi></msub></mrow></semantics></math></inline-formula>, were found <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>=</mo></mrow></semantics></math></inline-formula> 0.272 ± 0.001 (Voronoi) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>=</mo></mrow></semantics></math></inline-formula> 0.47 ± 0.02 (Poisson Line). The Shannon Entropy for the random Voronoi tessellation was calculated as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>=</mo></mrow></semantics></math></inline-formula> 1.690 ± 0.001 and for the Poisson line tessellation as <i>S</i> = 1.265 ± 0.015. The main contribution of the paper is the calculation of the Shannon entropy of the random point process and the establishment of the new bi-colored Ramsey graph on top of the tessellations.