Almost all graphs with 2.522 n edges are not 3-colorable

We prove that for $c \geq 2.522$ a random graph with $n$ vertices and $m=cn$ edges is not 3-colorable with probability $1-o(1)$. Similar bounds for non-$k$-colorability are given for $k>3$.

[1]  Darren Redfern,et al.  The Maple handbook , 1994 .

[2]  David A. Redfern,et al.  The Maple Handbook: Maple V Release 3 , 1995 .

[3]  A. Rbnyi.  ON THE EVOLUTION OF RANDOM GRAPHS , 2001 .

[4]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[5]  Colin McDiarmid,et al.  Topics in Chromatic Graph Theory: Colouring random graphs , 2015 .

[6]  Tomasz Łuczak,et al.  Size and connectivity of the k-core of a random graph , 1991 .

[7]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[8]  Michael Molloy,et al.  The analysis of a list-coloring algorithm on a random graph , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[9]  Yannis C. Stamatiou,et al.  Approximating the unsatisfiability threshold of random formulas , 1998, Random Struct. Algorithms.

[10]  Colin McDiarmid.  On a Correlation Inequality of Farr , 1992, Comb. Probab. Comput..

[11]  Béla Bollobás,et al.  The chromatic number of random graphs , 1988, Comb..

[12]  Tomasz Luczak,et al.  Size and connectivity of the k-core of a random graph , 1991, Discret. Math..

[13]  B. Bollobás.  The evolution of random graphs , 1984 .

[14]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[15]  E. Friedgut,et al.  Sharp thresholds of graph properties, and the -sat problem , 1999 .

[16]  Michael Molloy.  A gap between the appearances of a k-core and a (k+1)-chromatic graph , 1996, Random Struct. Algorithms.

[17]  Vasek Chvátal,et al.  Almost All Graphs with 1.44n Edges are 3-Colorable , 1991, Random Struct. Algorithms.

[18]  Ehud Friedgut,et al.  A Sharp Threshold for k-Colorability , 1999, Random Struct. Algorithms.

[19]  Joel H. Spencer,et al.  Sudden Emergence of a Giantk-Core in a Random Graph , 1996, J. Comb. Theory, Ser. B.