Access the full text.
Sign up today, get DeepDyve free for 14 days.
R. Isaacs (1975)
Infinite Families of Nontrivial Trivalent Graphs Which are not Tait ColorableAmerican Mathematical Monthly, 82
H. Hind (1990)
An improved bound for the total chromatic number of a graphGraphs Combin., 6
A. Cavicchioli, Mauro Meschiari, B. Ruini, F. Spaggiari (1998)
A survey on snarks and new results: Products, reducibility and a computer searchJ. Graph Theory, 28
S. Fiorini, Robin Wilson (1977)
Edge-colourings of graphs
E. Steffen (1998)
Classifications and characterizations of snarksDiscret. Math., 188
G. Brinkmann, E. Steffen (1998)
Snarks and ReducibilityArs Comb., 50
A. Chetwynd, J. Wilson (1981)
Snarks and supersnarks.
P. Sinclair (1997)
The construction and reduction of strong snarksDiscret. Math., 167-168
E. Steffen (1996)
Tutte's 5-flow conjecture for graphs of nonorientable genus 5J. Graph Theory, 22
P. Seymour (1981)
Nowhere-zero 6-flowsJ. Comb. Theory, Ser. B, 30
J. Petersen (1898)
Sur le théoréme de TaitL'intermédiaire des Mathématicien, 5
S. Grünewald, E. Steffen (1999)
Chromatic-index-critical graphs of even orderJ. Graph Theory, 30
R. Nedela, M. Skoviera (1996)
Decompositions and reductions of snarksJ. Graph Theory, 22
F. Jaeger (1988)
Selected Topics in Graph Theory
Baogang Xu (1998)
A sufficient condition for bipartite graphs to be type oneJ. Graph Theory, 29
H. Yap (1996)
Total Colourings of Graphs
A. G. Chetwynd, R. J. Wilson (1981)
Theory and Applications of Graphs
Michael Molloy, B. Reed (1998)
A Bound on the Total Chromatic NumberCombinatorica, 18
J. Collier, E. Schmeichel (1978)
Systematic searches for hypohamiltonian graphsNetworks, 8
Tommy Jensen, G. Royle (1999)
Hajós constructions of critical graphsJ. Graph Theory, 30
J. J. Watkins, R. J. Wilson (1991)
Graph Theory, Combinatorics, and Applications (Kalamazoo, MI, 1988)
M. Kochol (1996)
Snarks without Small CyclesJ. Comb. Theory, Ser. B, 67
G. Brinkmann, E. Steffen (1997)
3- and 4-critical Graphs of Small Even OrderDiscret. Math., 169
Jean-Luc Fouquet (1982)
Note sur la non existence d'un snark d'ordre 16Discret. Math., 38
H. Hind, Michael Molloy, B. Reed (1999)
Total Coloring With $\Delta + \mbox\lowercasepoly(\log \Delta)$ ColorsSIAM Journal on Computing, 28
R. Häggkvist, A. Chetwynd (1992)
Some upper bounds on the total and list chromatic numbers of multigraphsJ. Graph Theory, 16
E. Steffen (2001)
On bicritical snarksMathematica Slovaca, 51
M. Preissmann (1982)
Snarks of order 18Discret. Math., 42
H. Hind, M. Molloy (1999)
Total coloring with ( +poly log colorsSIAM J. Comput., 28
G. Brinkmann, E. Steffen (1998)
Chromatic-Index-Critical Graphs of Orders 11 and 12Eur. J. Comb., 19
Tommy Jensen, B. Toft (1994)
Graph Coloring Problems
Z. F. Zhang, J. F. Wang (1992)
The progress of total colorings of graphsAdv. in Math., 4
S. Grünewald, E. Steffen (1999)
Cyclically 5-edge connected non-bicritical critical snarksDiscuss. Math. Graph Theory, 19
Martin Möller, H. Carstens, G. Brinkmann (1988)
Nowhere-zero flows in low genus graphsJ. Graph Theory, 12
V. Vizing (1968)
SOME UNSOLVED PROBLEMS IN GRAPH THEORYRussian Mathematical Surveys, 23
E. Steffen (1999)
Non-Bicritical Critical SnarksGraphs and Combinatorics, 15
S. Fiorini (1983)
Graphs and Other Combinatorial Topics
Daniel Sanders, Yue Zhao (1999)
On total 9-coloring planar graphs of maximum degree sevenJ. Graph Theory, 31
E. Steffen (1996)
Counterexamples to a conjecture about bottlenecks in non-Tait-colourable cubic graphsDiscret. Math., 161
We report the most relevant results on the classification, up to isomorphism, of nontrivial simple uncolorable (i.e., the chromatic index equals 4) cubic graphs, called snarks in the literature. Then we study many classes of snarks satisfying certain additional conditions, and investigate the relationships among them. Finally, we discuss connections between the snark family and some significant conjectures of graph theory, and list some problems and open questions which arise naturally in this research.
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 5, 2004
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.