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(7)
Hajós' graphcoloring conjecture: Variations and counterexamples
Some Topics in Combinatorial Theory
UBER EINE KLASSI KATION DER STRECKENKOMPLEXE
Topology of seriesparallel networks1
A characterization of certain excludedminor classes of matroids
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A Property of 4Chromatic Graphs and some Remarks on Critical Graphs
A Property of 4Chromatic Graphs and some Remarks on Critical Graphs,10.1112/jlms/s127.1.85,Journal of The London Mathematical Societysecond Series,G
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A Property of 4Chromatic Graphs and some Remarks on Critical Graphs
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Citations: 120
)
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G. A. Dirac
Journal:
Journal of The London Mathematical Societysecond Series  J LONDON MATH SOCSECOND SER
, vol. s127, no. 1, pp. 8592, 1952
DOI:
10.1112/jlms/s127.1.85
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jlms.oxfordjournals.org
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Citation Context
(56)
...Conjecture 1.1 is trivially true for k ≤ 3, and reasonably easy for k = 4, as shown by Dirac [
5
] and Hadwiger himself [6]...
Neil Robertson
,
et al.
Hadwiger number and chromatic number for near regular degree sequences
...[
2
] independently proved that if G has no K4minor (socalled seriesparallel graphs) then G is 3colourable...
David R. Wood
.
Contractibility and the Hadwiger Conjecture
...This is a generalization of Hajos’ conjecture for graphs without a K4subdivision, which was proved independently by Hadwiger [16] and Dirac [
11
]...
Kenichi Kawarabayashi
,
et al.
Recognizing a Totally Odd K4subdivision, Parity 2disjoint Rooted Pat...
...A classic conjecture attributed to Haj´os was that if G is rchromatic, then G contains a subdivision of Kr. Dirac [
11
] verified the conjecture for r ≤ 4. In 1979, Catlin [10] noticed that the lexicographic product of C5 and K3 is an 8chromatic counterexample to the Haj´os Conjecture...
Michael O. AlbertsonDaniel
,
et al.
Crossings, colorings, and cliques
...The following theorem is well known from graph theory [
6
]...
Matthias Baumgart
.
Partitioning Bispanning Graphs into Spanning Trees
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Citations
(120)
Incidence et caractéristiques des intoxications aux inhibiteurs de cholinestérases
Wafa Masri
,
Ines Belwaer
,
Nozha Brahmi
,
Hayet Ghorbal
,
Abderrazek Hedhili
,
Amamou Mouldi
Journal:
Revue Francophone Des Laboratoires
, vol. 2011, no. 429, pp. 4146, 2011
Hadwiger number and chromatic number for near regular degree sequences
(
Citations: 1
)
Neil Robertson
,
ZiXia Song
Journal:
Journal of Graph Theory  JGT
, vol. 64, no. 3, pp. 175183, 2010
Independent paths and K5subdivisions
(
Citations: 1
)
Jie Ma
,
Xingxing Yu
Journal:
Journal of Combinatorial Theory  JCT
, vol. 100, no. 6, pp. 600616, 2010
Contractibility and the Hadwiger Conjecture
(
Citations: 1
)
David R. Wood
Journal:
European Journal of Combinatorics  EJC
, vol. 31, no. 8, pp. 21022109, 2010
Recognizing a Totally Odd K4subdivision, Parity 2disjoint Rooted Paths and a Parity Cycle Through Specified Elements
(
Citations: 1
)
Kenichi Kawarabayashi
,
Zhentao Lik
,
Bruce A. Reed
Conference:
ACMSIAM Symposium on Discrete Algorithms  SODA
, pp. 318328, 2010