Recent results on the total chromatic number

We give a survey of various recent results concerning the total chromatic number of simple graphs.

[1]  V. Chvátal.  On Hamilton's ideals , 1972 .

[2]  Anthony J. W. Hilton,et al.  Some refinements of the total chromatic number conjecture. , 1988 .

[3]  Lutz Volkmann,et al.  Class 1 conditions depending on the minimum degree and the number of vertices of maximum degree , 1990, J. Graph Theory.

[4]  Anthony J. W. Hilton,et al.  Recent progress on edge-colouring graphs , 1987, Discret. Math..

[5]  Colin McDiarmid,et al.  Total colouring regular bipartite graphs is NP-hard , 1994, Discret. Math..

[6]  Amanda G. Chetwynd,et al.  The Total Chromatic Number of Graphs of High Minimum Degree , 1991 .

[7]  Anthony J. W. Hilton,et al.  The Edge-Chromatic Class of Graphs with Maximum Degree at Least |V| – 3 , 1988 .

[8]  Anthony J. W. Hilton,et al.  1-factorizing Regular Graphs of High Degree - an Improved Bound , 1989, Discret. Math..

[9]  Wang Jianfang,et al.  Total chromatic number of graphs of high degree , 1989 .

[10]  Roland Häggkvist,et al.  Some upper bounds on the list and total chromatic numbers of multigraphs. , 1992 .

[11]  Anthony J. W. Hilton.  A total-chromatic number analogue of plantholt's theorem , 1990, Discret. Math..

[12]  H. Ryser.  A combinatorial theorem with an application to latin rectangles , 1951 .

[13]  Anthony J. W. Hilton,et al.  The total chromatic number of nearly complete bipartite graphs , 1991, J. Comb. Theory, Ser. B.

[14]  Hao Li,et al.  Hamiltonism, degree sum and neighborhood intersections , 1991, Discret. Math..

[15]  Dean G. Hoffman,et al.  The chromatic index of complete multipartite graphs , 1992, J. Graph Theory.

[16]  Anthony J. W. Hilton,et al.  The total chromatic number of graphs having large maximum degree , 1993, Discret. Math..

[17]  Anthony J. W. Hilton.  Two conjectures on edge-colouring , 1989, Discret. Math..

[18]  Abddn SANCHEZ-ARROYO,et al.  Determining the total colouring number is np-hard , 1989, Discret. Math..

[19]  H. R. Hind,et al.  An upper bound for the total chromatic number , 1990, Graphs Comb..

[20]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[21]  I Z Mitsova,et al.  [Role of Fe-Mo-cofactor in the formation of the catalytically active ATPase center of nitrogenase]. , 1980, Doklady Akademii nauk SSSR.

[22]  Hung-Lin Fu,et al.  Total colorings of graphs of order 2n having maximum degree 2n−2 , 1992, Graphs Comb..

[23]  Anthony J. W. Hilton,et al.  The total chromatic number of regular graphs whose complement is bipartite , 1994, Discret. Math..

[24]  A. Hilton,et al.  Star multigraphs with three vertices of maximum degree , 1986 .

[25]  Anthony J. W. Hilton,et al.  The chromatic index of graphs with large maximum degree, where the number of vertices of maximum degree is relatively small , 1990, J. Comb. Theory, Ser. B.

[26]  Bruce A. Reed,et al.  On Total Colorings of Graphs , 1993, J. Comb. Theory, Ser. B.

[27]  H. R. Hind.  An upper bound for the total chromatic number of dense graphs , 1992, J. Graph Theory.