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Investigation on Interval Edge-Colorings of Graphs

1994
*
Journal of combinatorial theory. Series B (Print)
*

An

doi:10.1006/jctb.1994.1053
fatcat:xmm33szzmjf6nejn7mnyohlhnq
*edge*-*coloring**of*a simple*graph*G with*colors*! ... . , t is called an*interval*t-*coloring*[3] if at least*one**edge**of*G is*colored*by*color*i, i = 1, ... , t and the*edges*incident with each vertex x are*colored*by dG(x) consecutive*colors*, where dG(x) ... ACKNOWLEDGMENT We appreciate all the suggestions*of*the referees. In particular, we would like to mention that Theorem 2 has been improved by*one**of*the referees. ...##
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Interval cyclic edge-colorings of graphs

2016
*
Discrete Mathematics
*

In this paper some properties

doi:10.1016/j.disc.2016.01.023
fatcat:rir7emlhwzaqnl5ng2qgh634au
*of**interval*cyclic*edge*-*colorings*are*investigated*. ... A proper*edge*-*coloring**of*a*graph*G with*colors*1, , t is called an*interval*cyclic t *coloring*if all*colors*are used, and the*edges*incident to each vertex ( ) v V G are*colored*with ( ) G d v consecutive ... obtained an upper bound*on*( ) W G for an*interval**colorable**graph*G depending*on*the number*of*vertices*of*G . ...##
###
On interval edge-colorings of complete tripartite graphs

2013
*
Ninth International Conference on Computer Science and Information Technologies Revised Selected Papers
*

An

doi:10.1109/csitechnol.2013.6710340
fatcat:gsxfoiplazabrm7qaeu6ba6ztu
*edge*-*coloring**of*a*graph*G with*colors*1, . . . , t is an*interval*t-*coloring*if all*colors*are used, and the*colors**of**edges*incident to each vertex*of*G are distinct and form an*interval**of*integers ... A*graph*G is*interval**colorable*if it has an*interval*t-*coloring*for some positive integer t. ... In [12] , Petrosyan*investigated**interval**colorings**of*complete*graphs*and n-dimensional cubes. ...##
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Interval edge-colorings of graph products
[article]

2012
*
arXiv
*
pre-print

In this paper

arXiv:1110.1165v2
fatcat:soebc3bxzfhmdiqgnjb4ckhhs4
*interval**edge*-*colorings**of*various*graph*products are*investigated*. ... An*interval*t-*coloring**of*a*graph*G is a proper*edge*-*coloring**of*G with*colors*1,2,...,t such that at least*one**edge**of*G is*colored*by i, i=1,2,... ... In this paper*interval**edge*-*colorings**of*various*graph*products are*investigated*. ...##
###
On interval edge-colorings of outerplanar graphs
[article]

2013
*
arXiv
*
pre-print

An

arXiv:1303.1039v1
fatcat:asc4ydc2qnaqhcmo27k243zhfi
*edge*-*coloring**of*a*graph*$G$ with*colors*$1,\ldots,t$ is called an*interval*$t$-*coloring*if all*colors*are used, and the*colors**of**edges*incident to any vertex*of*$G$ are distinct and form an*interval*... For an*interval**colorable**graph*$G$, the least value*of*$t$ for which $G$ has an*interval*$t$-*coloring*is denoted by $w(G)$. ... In [ 6] , Kamalian*investigated**interval**colorings**of*complete bipartite*graphs*and trees. ...##
###
Interval cyclic edge-colorings of graphs
[article]

2014
*
arXiv
*
pre-print

A proper

arXiv:1411.0290v1
fatcat:itxc5amlqzg35ipmg6jp5m6pea
*edge*-*coloring**of*a*graph*G with*colors*1,... ... We also obtain bounds*on*w_c(G) and W_c(G) for various classes*of**graphs*. Finally, we give some methods for constructing*of**interval*cyclically non-*colorable**graphs*. ... Acknowledgement We would like to thank the organizers*of*7-th Cracow conference*on**Graph*Theory "Rytro' 14"for the nice environment and working atmosphere at the conference. ...##
###
Interval edge coloring of a graph with forbidden colors

1993
*
Discrete Mathematics
*

We consider herein a problem

doi:10.1016/0012-365x(93)90546-6
fatcat:lwhyhj2mejci3lledzkfpfolke
*of**interval**coloring*the*edges**of*a*graph*under the restriction that certain*colors*cannot be used for some*edges*. ... .,*Interval**edge**coloring**of*a*graph*with forbidden*colors*, Discrete Mathematics 121 (1993) 135-143. This paper is complementary to Kubale (1989) . ... If G is a uninomial bipartite*graph*and F is such that all*edges*with forbidden*colors*have*one*permissible*interval**of**colors*and are incident to*one*vertex*of*maximum degree, then a chromatic*coloring*...##
###
Interval edge-colorings of K_1,m,n
[article]

2013
*
arXiv
*
pre-print

In this note we prove that K_1,m,n is

arXiv:1308.4431v1
fatcat:eeinz2xitrepfezri57d6kb54i
*interval**edge*-*colorable*if and only if gcd(m+1,n+1)=1. It settles in the affirmative a conjecture*of*Petrosyan. ... In [13] , Petrosyan*investigated**interval**colorings**of*complete*graphs*and n-dimensional cubes. ... Recently, Petrosyan*investigated**interval**edge*-*colorings**of*complete multipartite*graphs*. In particular, he proved [12] the following result: Theorem 5. If K n,... ...##
###
Interval edge-colorings of complete graphs and n-dimensional cubes

2010
*
Discrete Mathematics
*

An

doi:10.1016/j.disc.2010.02.001
fatcat:hjrfmhnt6rgjxjivjgjd6ucf7e
*edge*-*coloring**of*a*graph*G with*colors*1, 2, . . . , t is called an*interval*t-*coloring*if for each i ∈ {1, 2, . . . , t} there is at least*one**edge**of*G*colored*by i, and the*colors**of**edges*incident ... to any vertex*of*G are distinct and form an*interval**of*integers. ... For non-bipartite*graphs*, the problems*of*existence, construction, and bounds*on*the numbers*of**colors*in*interval**colorings*were*investigated*in [1] [2] [3] 5, 10, 17, 19, 21] . ...##
###
Page 2566 of Mathematical Reviews Vol. , Issue 95e
[page]

1995
*
Mathematical Reviews
*

(AR-AOS-C; Erevan)

*Investigation**on**interval**edge*-*colorings**of**graphs*. (English summary) J. Combin. Theory Ser. B 62 (1994), no. 1, 34-43. ... An*edge**coloring**of*a*graph*G with*colors*1,2,---,¢ is an*interval*t-*coloring*if each*color*is used at least once and for each node x the*edges*adjacent to x are*colored*with dg(x) consecutive*colors*( ...##
###
Interval edge colorings of some products of graphs

2011
*
Discussiones Mathematicae Graph Theory
*

An

doi:10.7151/dmgt.1551
fatcat:jls7gpyhtzbgljorionoc6pq7a
*edge**coloring**of*a*graph*G with*colors*1, 2, . . . , t is called an*interval*t-*coloring*if for each i ∈ {1, 2, . . . , t} there is at least*one**edge**of*G*colored*by i, and the*colors**of**edges*incident ... A*graph*G is*interval**colorable*, if there is an integer t ≥ 1 for which G has an*interval*t-*coloring*. ... There are many papers [17, 24, 26, 27, 28, 31, 38] devoted to*edge**colorings**of*various products*of**graphs*. In this paper we*investigate**interval**edge**colorings**of*various products*of**graphs*. ...##
###
Interval colorings of complete balanced multipartite graphs
[article]

2012
*
arXiv
*
pre-print

,t is an

arXiv:1211.5311v1
fatcat:djw3fzfug5gitfajuxzz4fpgtq
*interval*t-*coloring*if all*colors*are used, and the*colors**of**edges*incident to each vertex*of*G are distinct and form an*interval**of*integers. ... A complete k-partite*graph*G is a complete balanced k-partite*graph*if |V_1| = |V_2| =... = |V_k|. An*edge*-*coloring**of*a*graph*G with*colors*1,... ... In [ 10] , Kamalian*investigated**interval**colorings**of*complete bipartite*graphs*and trees. ...##
###
Interval edge-colorings of composition of graphs
[article]

2015
*
arXiv
*
pre-print

An

arXiv:1508.00158v1
fatcat:vootp26wazbrdfgjuawpl5ajqi
*edge*-*coloring**of*a*graph*G with consecutive integers c_1,... ... ,c_t is called an*interval*t-*coloring*if all*colors*are used, and the*colors**of**edges*incident to any vertex*of*G are distinct and form an*interval**of*integers. ... Acknowledgement We would like to thank Hrant Khachatrian for his constructive suggestions*on*improvements*of*the paper. ...##
###
Interval edge-colorings of cubic graphs
[article]

2011
*
arXiv
*
pre-print

,t is called an

arXiv:1110.1161v1
fatcat:tpbwlrrvnrcz5cc4aucpycwnia
*interval*t-*coloring*if all*colors*are used, and the*colors**of**edges*incident to any vertex*of*G are distinct and form an*interval**of*integers. ... An*edge*-*coloring**of*a multigraph G with*colors*1,2,... ... If is a connected planar*graph*and G G ∈ N , then 11 ( ) . 6 ( ) V G W G ≤ In this paper we*investigate**interval**edge*-*colorings**of*cubic*graphs*and multigraphs. ...##
###
Precoloring extension on unit interval graphs

2006
*
Discrete Applied Mathematics
*

Comput. 5 (1) (1996) 35-56], we show that the precoloring extension problem is NP-complete

doi:10.1016/j.dam.2005.10.008
fatcat:i22yai3zebfv7dbknybm6nu72a
*on*unit*interval**graphs*. ... In the precoloring extension problem a*graph*is given with some*of*the vertices having preassigned*colors*and it has to be decided whether this*coloring*can be extended to a proper k-*coloring**of*the*graph*... Acknowledgements I am grateful to Katalin Friedl, Judit Csima, and the two anonymous referees for their comments that improved the presentation*of*the paper. ...
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