Geodesic
Critical Erd\H os and Dirac graphs of even degree
Diskretnyj analiz i issledovanie operacij, Tome 10 (2003) no. 3, pp. 12-22.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{DA_2003_10_3_a1,
     author = {A. A. Dobrynin and L. S. Mel'nikov and A. V. Pyatkin},
     title = {Critical {Erd\H} os and {Dirac} graphs of even degree},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {12--22},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2003_10_3_a1/}
}
TY  - JOUR
AU  - A. A. Dobrynin
AU  - L. S. Mel'nikov
AU  - A. V. Pyatkin
TI  - Critical Erd\H os and Dirac graphs of even degree
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2003
SP  - 12
EP  - 22
VL  - 10
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2003_10_3_a1/
LA  - ru
ID  - DA_2003_10_3_a1
ER  - 
%0 Journal Article
%A A. A. Dobrynin
%A L. S. Mel'nikov
%A A. V. Pyatkin
%T Critical Erd\H os and Dirac graphs of even degree
%J Diskretnyj analiz i issledovanie operacij
%D 2003
%P 12-22
%V 10
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2003_10_3_a1/
%G ru
%F DA_2003_10_3_a1
A. A. Dobrynin; L. S. Mel'nikov; A. V. Pyatkin. Critical Erd\H os and Dirac graphs of even degree. Diskretnyj analiz i issledovanie operacij, Tome 10 (2003) no. 3, pp. 12-22. http://geodesic.mathdoc.fr/item/DA_2003_10_3_a1/

[1] Geri M., Dzhonson D., Vychislitelnye mashiny i trudnoreshaemye zadachi, Mir, M., 1982 | MR

[2] Dobrynin A. A., Melnikov L. S., Pyatkin A. V., “4-khromaticheskie reberno-kriticheskie regulyarnye grafy s vysokoi svyaznostyu”, Rossiiskaya konf. “Diskretnyi analiz i issledovanie operatsii”, Materialy konferentsii (Novosibirsk, 24–28 iyunya 2002 g.), Izd-vo In-ta matematiki, Novosibirsk, 2002, 25–30

[3] Evstigneev V. A., Melnikov L. S., Zadachi i uprazhneniya po teorii grafov i kombinatorike, NGU, Novosibirsk, 1981 | MR

[4] Brooks R. L., “On colouring the nodes of a network”, Proc. Cambridge Phil. Soc., 37 (1941), 194–197 | DOI | MR | Zbl

[5] Chao C. Y., “A critically chromatic graph”, Discrete Math., 172:1–3 (1997), 3–7 | DOI | MR | Zbl

[6] Dirac G. A., “4-chrome Graphen Trennende und vollständige 4-Graphen”, Math. Nachr., 22:1–2 (1960), 51–60 | DOI | MR | Zbl

[7] Dirac G. A., “In abstrakten Graphen vorhandene vollständige 4-Graphen und ihre Unterteilungen”, Math. Nachr., 22:1–2 (1960), 61–85 | DOI | MR | Zbl

[8] Dobrynin A. A., Melnikov L. S., Pyatkin A. V., “On 4-chromatic edgecritical regular graphs of high connectivity”, Discrete Math., 260:1–3 (2003), 315–319 | DOI | MR | Zbl

[9] Dobrynin A. A., Melnikov L. S., Pyatkin A. V., “Regular 4-critical graphs of even degree”, J. Graph Theory, submitted | MR

[10] Dobrynin A. A., Melnikov L. S., Pyatkin A. V., “Computer search for regular 4-critical graphs”, J. Combin. Math. Combin. Comput., submitted

[11] Erdös P., “On some aspects of my work with Gabriel Dirac”, Graph Theory in Memory of G. A. Dirac, Annals of Discrete Mathematics, 41, North-Holland, Amsterdam, 1989, 111–116 | MR

[12] Gallai T., “Kritische Graphen I”, Publ. Math. Inst. Hungar. Acad. Sci., 8:1–2 (1963), 165–192 | MR | Zbl

[13] Göbel F., Neutel E. A., “Cyclic graphs”, Discrete Appl. Math., 99:1–3 (2000), 3–12 | DOI | MR | Zbl

[14] Jensen T. R., “Dense critical and vertex-critical graphs”, Discrete Math., 258:1–3 (2002), 63–84 | DOI | MR | Zbl

[15] Jensen T. R., Royle G. F., “Small graphs with chromatic number 5: a computer search”, J. Graph Theory, 19:1 (1995), 107–116 | DOI | MR | Zbl

[16] Jensen T., Toft B., Graph Coloring Problems, JohnWiley Sons, New York, 1995 | MR | Zbl

[17] Koester G., “Note to a problem of T. Gallai and G. A. Dirac”, Combinatorica, 5:3 (1985), 227–228 | DOI | MR | Zbl

[18] Koester G., “4-critical 4-valent planar graphs constructed with crowns”, Math. Scand., 67 (1990), 15–22 | MR | Zbl

[19] Mader W., “Über den Zusammenhäng symmetrischer Graphen”, Arch. Math. (Basel), 21:3 (1970), 331–336 | MR | Zbl

[20] Mader W., “Eine Eigenschaft der Atome endlicher Graphen”, Arch. Math. (Basel), 22:3 (1971), 333–336 | MR

[21] Pyatkin A. V., “6-regular 4-critical graph”, J. Graph Theory, 41:4 (2002), 286–291 | DOI | MR | Zbl

[22] Watkins M. E., “Some classes of hypoconnected vertex-transitive graphs”, Recent Progress in Combinatorics, Academic Press, New York, 1969, 323–328 | MR

[23] Watkins M. E., “Connectivity of transitive graphs”, J. Combin. Theory, 8:1 (1970), 23–29 | DOI | MR | Zbl

[24] Youngs D. A., “Gallai's problem on Dirac's construction”, Discrete Math., 101:1–3 (1992), 343–350 | DOI | MR | Zbl