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Coloring some classes of mixed graphs

B. Ries
2007 Discrete Applied Mathematics  
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

Zsolt Tuza, Vitaly Voloshin, Huishan Zhou
2002 Discrete Mathematics  
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

Amanda Montejano, Pascal Ochem, Alexandre Pinlou, André Raspaud, Éric Sopena
2010 Discrete Applied Mathematics  
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

Amanda Montejano, Pascal Ochem, Alexandre Pinlou, André Raspaud, Éric Sopena
2008 Electronic Notes in Discrete Mathematics  
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  
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

B. Ries, D. de Werra
2008 European journal of combinatorics (Print)  
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  
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

Hajo J. Broersma, Agostino Capponi, Daniël Paulusma
2008 SIAM Journal on Discrete Mathematics  
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

Zsolt Tuza
2019 The Art of Discrete and Applied Mathematics  
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  
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  
,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

Amanda Montejano, Alexandre Pinlou, André Raspaud, Éric Sopena
2009 Electronic Notes in Discrete Mathematics  
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

Jaroslav Nešetřil, André Raspaud
2000 Journal of combinatorial theory. Series B (Print)  
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  
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]

Marthe Bonamy, Nicolas Bousquet
2014 arXiv   pre-print
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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