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Abstract: Homomorphisms between graphs are studied as a generalization of colorings and of chromatic number. We investigate here homomorphisms from orientations of undirected planar graphs to graphs (not necessarily planar) containing as few digons as possible. We relate the existence of such homomorphisms to girth and it appears that these questions remain interesting even under large girth assumption in the range where the chromatic number is an easy invariant. (Update)
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BibTeX entry: (Update)
J. Nesetril, A. Raspaud and E. Sopena, Colorings and girth of oriented planar graphs, Research Report 1084-95, Universit'e Bordeaux I (1995). http://citeseer.ist.psu.edu/nesetril95colorings.html More
@article{ nesetril97colorings,
author = "J. {Nesetril} and A. {Raspaud} and E. {Sopena}",
title = "Colorings and girth of oriented planar graphs",
journal = "Discrete Math.",
volume = "165-166",
pages = "519--530",
year = "1997",
url = "citeseer.ist.psu.edu/nesetril95colorings.html" }
Citations (may not include all citations):151 Every planar map is four colorable (context) - Appel, Haken - 1976
49 Good and semi-strong colorings of oriented planar graphs - Raspaud, Sopena - 1994
49 The chromatic number of oriented graphs - Sopena - 1995
43 On acyclic coloring of planar graphs (context) - Borodin - 1979
31 Duality and polynomial testing of tree homomorphisms (context) - Hell, Nesetril et al.
18 Bolyai Society Mathematical Studies (context) - Hell, Nesetril et al. - 1994
15 Acyclic colorings of planar graphs (context) - Grunbaum - 1973
12 Ein Dreifarbensatz fur dreikreisfreie Netze auf der Kuzel (context) - Grotzsch - 1959
11 Colorings and interpretations : a connection between graphs .. (context) - Maurer, Salomaa et al. - 1981
6 work in preparation (context) - Borodin, Kostochka et al. - 1995
5 Universality of A-mote graphs (context) - Haggkvist, Hell - 1993
4 Some new good characterizations of directed graphs (context) - Kom'arek - 1984
4 On bounded treewidth duality of graphs - Nesetril, Zhu - 1994
4 Acyclic 6-coloring of planar graphs (context) - Kostochka - 1976
2 The complexity of colorings by semicomplete digraphs (context) - Bang-Jensen, Hell et al. - 1988
2 On universal planar oriented graphs and finitely generated c.. (context) - Nesetril, Raspaud et al.
2 Acyclic and oriented chromatic numbers (context) - Sopena, Zhu
2 Grotzsch 3-color theorem and its counterparts for the torus .. (context) - Thomassen - 1994
1 The effect of two cycles on the complexity of colourings by .. (context) - Bang-Jensen, Hell - 1990
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