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Coloring some classes of mixed graphs

2007
*
Discrete Applied Mathematics
*

We consider the

doi:10.1016/j.dam.2006.05.004
fatcat:da52wb6a5vhzvds6puywbtdyui
*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*. ...##
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Uniquely colorable mixed hypergraphs

2002
*
Discrete Mathematics
*

The

doi:10.1016/s0012-365x(01)00176-5
fatcat:jijcfyq6xrgadgy3vbusi7neba
*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. ...##
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Homomorphisms of 2-edge-colored graphs

2010
*
Discrete Applied Mathematics
*

We consider various

doi:10.1016/j.dam.2009.09.017
fatcat:tl4c2ayaprfujgckaitrjdfzsi
*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) . ...##
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Homomorphisms of 2-edge-colored graphs

2008
*
Electronic Notes in Discrete Mathematics
*

We consider various

doi:10.1016/j.endm.2008.01.007
fatcat:cipqqal6f5czbhnbkbjra5otdy
*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) . ...##
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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*. ...##
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On two coloring problems in mixed graphs

2008
*
European journal of combinatorics (Print)
*

Ries,

doi:10.1016/j.ejc.2007.03.006
fatcat:pocdhsh5izfrdiieouoqtu5igi
*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. ...##
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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. ...##
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A New Algorithm for On-line Coloring Bipartite Graphs

2008
*
SIAM Journal on Discrete Mathematics
*

In order to have

doi:10.1137/060668675
fatcat:d2w372ysqfduxmjqokajheduia
*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. ...##
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Mixed hypergraphs and beyond

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. ...

##
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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 ...##
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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>,... ...##
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Chromatic number of sparse colored mixed planar graphs

2009
*
Electronic Notes in Discrete Mathematics
*

The chromatic number

doi:10.1016/j.endm.2009.07.060
fatcat:wzhz7hasdzhk3n6ph7vg2tnhqm
*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 ...##
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Colored Homomorphisms of Colored Mixed Graphs

2000
*
Journal of combinatorial theory. Series B (Print)
*

Let T be the

doi:10.1006/jctb.2000.1977
fatcat:i3pycpz4obeyjmacwxjqute7nu
*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. ...##
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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. ...##
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Recoloring graphs via tree decompositions
[article]

2014
*
arXiv
*
pre-print

The

arXiv:1403.6386v1
fatcat:ocsgjngk75gc7bmugne7hjdppi
*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. ...
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