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Coloring some classes of mixed graphs
2007
Discrete Applied Mathematics
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We consider the coloring problem for mixed graphs, that is, for graphs containing edges and arcs. ...
In this paper, we will consider some special classes of graphs and analyse the complexity status of the mixed graph coloring problem for these classes. ...
We gave some complexity results on that problem for some special classes of graphs. ...
doi:10.1016/j.dam.2006.05.004
fatcat:da52wb6a5vhzvds6puywbtdyui
Uniquely colorable mixed hypergraphs
2002
Discrete Mathematics
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The class of these "weakly uniquely colorable" mixed hypergraphs contains all uniquely colorable graphs in the usual sense. ...
In particular, we show that every colorable mixed hypergraph can be embedded into some uniquely colorable mixed hypergraph; we investigate the role of uniquely colorable subhypergraphs being separators ...
A mixed hypergraph H is called It follows from the deÿnitions that in mixed hypergraphs in each feasible partition of X into color classes the union of any two color classes contains some D-edge. ...
doi:10.1016/s0012-365x(01)00176-5
fatcat:jijcfyq6xrgadgy3vbusi7neba
Homomorphisms of 2-edge-colored graphs
2010
Discrete Applied Mathematics
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We consider various graph classes (outerplanar graphs, partial 2-trees, partial 3-trees, planar graphs) and the problem is to find, for each class, the smallest number of vertices of a 2-edge-colored graph ...
In this paper, we study homomorphisms of 2-edge-colored graphs, that is graphs with edges colored with two colors. ...
∪E m (G) of the edges of G, where E j (G) contains all edges with color j. We denote the class of (n, m)-mixed graphs by G (n,m) . ...
doi:10.1016/j.dam.2009.09.017
fatcat:tl4c2ayaprfujgckaitrjdfzsi
Homomorphisms of 2-edge-colored graphs
2008
Electronic Notes in Discrete Mathematics
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We consider various graph classes (outerplanar graphs, partial 2-trees, partial 3-trees, planar graphs) and the problem is to find, for each class, the smallest number of vertices of a 2-edge-colored graph ...
In this paper, we study homomorphisms of 2-edge-colored graphs, that is graphs with edges colored with two colors. ...
∪E m (G) of the edges of G, where E j (G) contains all edges with color j. We denote the class of (n, m)-mixed graphs by G (n,m) . ...
doi:10.1016/j.endm.2008.01.007
fatcat:cipqqal6f5czbhnbkbjra5otdy
Page 4923 of Mathematical Reviews Vol. , Issue 2003g
[page]
2003
Mathematical Reviews
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It is easy to see that a color critical graph is star color critical. In this paper the author gives two infinite classes of planar graphs which are star color critical but not color critical. ...
The ordinary graphs that are uc mixed hypergraphs are only the complete graphs, but wuc mixed hypergraphs generalize the usual notion of uniquely colorable graphs. ...
On two coloring problems in mixed graphs
2008
European journal of combinatorics (Print)
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Ries, Coloring some classes of mixed graphs, Discrete Applied Mathematics 155 (2007) 1-6]. ...
We are interested in coloring the vertices of a mixed graph, i.e., a graph containing edges and arcs. ...
Werner for helpful discussions and remarks as well as two anonymous referees for their comments which improved the presentation of the paper. ...
doi:10.1016/j.ejc.2007.03.006
fatcat:pocdhsh5izfrdiieouoqtu5igi
Page 767 of Mathematical Reviews Vol. , Issue 2001B
[page]
2001
Mathematical Reviews
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Summary: “We discuss some recent results in coloring of mixed hypergraphs. Namely, we provide results on mixed interval hyper- graphs and show how they are generalized on mixed hypertrees. ...
(MO-AOS-MI; Chisinau) Some results on coloring of mixed hypergraphs. (English summary) Sth Workshop on Combinatorics (Messina, 1999). Rend. Sem. Mat. Messina Ser. ...
A New Algorithm for On-line Coloring Bipartite Graphs
2008
SIAM Journal on Discrete Mathematics
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In order to have some measure of the performance of on-line algorithms, the notion of competitive algorithms has been introduced in [20] and specifically for coloring in [9] . ...
Solving this subproblem can be particularly useful if somebody must design an on-line coloring algorithm in the case that the input graphs are only known to be in a specified class of graphs. ...
We thank the anonymous referees for their useful comments on an earlier version of this paper. ...
doi:10.1137/060668675
fatcat:d2w372ysqfduxmjqokajheduia
Mixed hypergraphs and beyond
2019
The Art of Discrete and Applied Mathematics
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Some open problems are collected on hypergraphs, graphs, and designs, presented at the HyGraDe conference celebrating Mario Gionfriddo's 70 th birthday. ...
Graphs There are many problems in graph theory which can be interpreted in terms of colorings of mixed hypergraphs. Here we discuss only one of them. F-WORM colorings. ...
of the color classes might occur. ...
doi:10.26493/2590-9770.1234.37b
fatcat:ielyamrspjftbftru2src2etza
Page 7043 of Mathematical Reviews Vol. , Issue 2002J
[page]
2002
Mathematical Reviews
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The new method is applied to analyze the mixing time of the Glauber dynamics for graph colorings. ...
“Some of the edges adjacent to a specific pair of opposite vertices of an /-regular bipartite graph are already colored with S colors that appear only on one edge (single colors) and D colors using at ...
Page 8948 of Mathematical Reviews Vol. , Issue 2003m
[page]
2003
Mathematical Reviews
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,S, if each color class is a d-dominating set of every factor. ...
A d-domatic coloring of G is a coloring of V such that each color class is a d-dominating set of G. The coloring is an all-factor d-domatic coloring of G with respect to S;,.S>,... ...
Chromatic number of sparse colored mixed planar graphs
2009
Electronic Notes in Discrete Mathematics
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The chromatic number of such a graph G is defined as the smallest order of a colored mixed graph H such that there exists a (arc-color preserving) homomorphism from G to H. ...
We study in this paper the colored mixed chromatic number of planar graphs, partial 2-trees and outerplanar graphs with given girth. ...
Concerning the class of (0, 2)-colored mixed graphs, the authors in [4] recently bounded the (0, 2)-colored mixed chromatic number of planar graphs, partial 2trees and outerplanar graphs with given girth ...
doi:10.1016/j.endm.2009.07.060
fatcat:wzhz7hasdzhk3n6ph7vg2tnhqm
Colored Homomorphisms of Colored Mixed Graphs
2000
Journal of combinatorial theory. Series B (Print)
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Let T be the class of (n, m)-colored mixed forests: /(T, n, 0)=2n+1. (1) /(T, n, m)=2 \ n+ \ m 2 +1 + for m{0. (2) Theorem 1.2. ...
Proof of Theorem 1.2 Let K 2n+m, 2n+m be a complete bipartite mixed graph with 2n+m vertices in each bipartition class, defined as follows. ...
doi:10.1006/jctb.2000.1977
fatcat:i3pycpz4obeyjmacwxjqute7nu
Page 57 of Mathematical Reviews Vol. , Issue 2000a
[page]
2000
Mathematical Reviews
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A mixed hypergraph is called uniquely colorable if it has exactly one coloring apart from the permutation of colors. ...
The minimum [maximum] number of colors for which there exists a coloring of a mixed hypergraph H using all the colors is called the lower [upper] chromatic number. ...
Recoloring graphs via tree decompositions
[article]
2014
arXiv
pre-print
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The graph classes are also optimal in some sense: one of the smallest interesting superclass of distance-hereditary graphs corresponds to comparability graphs, for which no such property holds (even when ...
A graph is k-mixing if any proper k-coloring can be transformed into any other through a sequence of adjacent proper k-colorings. ...
The class of k-degenerate graphs also contains some sub-classes that are themselves interesting. One of the most famous is the class of planar graphs (which are 5-degenerate). Conjecture 18. ...
arXiv:1403.6386v1
fatcat:ocsgjngk75gc7bmugne7hjdppi
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