Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 25
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Alon, Noga and Ben-Eliezer, Omri 2016. Local and global colorability of graphs. Discrete Mathematics, Vol. 339, Issue. 2, p. 428.

    Ben-Eliezer, Ido Kaufman, Tali Krivelevich, Michael and Ron, Dana 2013. Comparing the strength of query types in property testing: The case of k-colorability. computational complexity, Vol. 22, Issue. 1, p. 89.

    Harutyunyan, Ararat and Mohar, Bojan 2012. Two results on the digraph chromatic number. Discrete Mathematics, Vol. 312, Issue. 10, p. 1823.

    Rubinfeld, Ronitt and Shapira, Asaf 2011. Sublinear Time Algorithms. SIAM Journal on Discrete Mathematics, Vol. 25, Issue. 4, p. 1562.

    2011. Graph Coloring Problems.

    2011. Graph Coloring Problems.

    Chierichetti, Flavio and Vattani, Andrea 2010. The Local Nature of List Colorings for Graphs of High Girth. SIAM Journal on Computing, Vol. 39, Issue. 6, p. 2232.

    Czyzowicz, J. Dobrev, S. Kranakis, E. Opatrny, J. and Urrutia, J. 2009. Local edge colouring of Yao-like subgraphs of Unit Disk Graphs. Theoretical Computer Science, Vol. 410, Issue. 14, p. 1388.

    Chvátal, V. 2007. Almost all graphs with 1.44n edges are 3-colorable. Random Structures & Algorithms, Vol. 2, Issue. 1, p. 11.

    Arora, S. Bollobas, B. and Lovasz, L. 2002. The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.. p. 313.

    Bogdanov, A. Obata, K. and Trevisan, L. 2002. The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.. p. 93.

    Brightwell, G. R. and Kohayakawa, Y. 1993. Ramsey properties of orientations of graphs. Random Structures and Algorithms, Vol. 4, Issue. 4, p. 413.

    Steinberg, Richard 1993. Quo Vadis, Graph Theory? - A Source Book for Challenges and Directions.

    Chvátal, V. Cook, W. and Hartmann, M. 1989. On cutting-plane proofs in combinatorial optimization. Linear Algebra and its Applications, Vol. 114-115, p. 455.

    Sachs, Horst and Stiebitz, Michael 1989. Graph Colouring and Variations.

    Sachs, Horst and Stiebitz, Michael 1989. On constructive methods in the theory of colour-critical graphs. Discrete Mathematics, Vol. 74, Issue. 1-2, p. 201.

    Erdös, Paul Faudree, Ralph Pach, János and Spencer, Joel 1988. How to make a graph bipartite. Journal of Combinatorial Theory, Series B, Vol. 45, Issue. 1, p. 86.

    El-Zahar, M. and Erdős, P. 1985. On the existence of two non-neighboring subgraphs in a graph. Combinatorica, Vol. 5, Issue. 4, p. 295.

    Chvátal, V. 1984. Probabilistic methods in graph theory. Annals of Operations Research, Vol. 1, Issue. 3, p. 171.

    McDiarmid, Colin 1984. Colouring random graphs. Annals of Operations Research, Vol. 1, Issue. 3, p. 183.


On circuits and subgraphs of chromatic graphs

  • P. Erdös (a1)
  • DOI:
  • Published online: 01 February 2010

A graph is said to be k-chromatic if its vertices can be split into k classes so that two vertices of the same class are not connected (by an edge) and such a splitting is not possible for k−1 classes. Tutte was the first to show that for every k there is a k-chromatic graph which contains no triangle [1].

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

2. J. B. Kelly and L. M. Kelly , “Paths and circuits in critical graphs”, American J. of Math., 76 (1954), 786792.

3. P. Erdös , “Graph theory and probability”, Canadian J. of Math., 11 (1959), 3438.

5. P. Erdös and G. Szekeres , “Graph theory and probability (II)”, Canadian J. of Math., 13 (1961), 346352.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
Please enter your name
Please enter a valid email address
Who would you like to send this to? *