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Cooperative colorings of trees and of bipartite graphs [article]

Ron Aharoni, Eli Berger, Maria Chudnovsky, Frédéric Havet, Zilin Jiang
2020 arXiv   pre-print
We prove that Ω(loglog d) < m_T(d) < O(log d) and Ω(log d)< m_B(d) < O(d/log d), where T is the class of trees and B is the class of bipartite graphs.  ...  ,G_m) of graphs on the same vertex set V, a cooperative coloring is a choice of vertex sets I_1, ... ,I_m, such that I_j is independent in G_j and _j=1^mI_j = V.  ...  The rest of the paper is organized as follows. In Section 2 and Section 3, we prove Theorem 3 for trees and bipartite graphs respectively.  ... 
arXiv:1806.06267v2 fatcat:gww2t5gkzbagvhj64x2yabozfe

Cooperative Colorings of Trees and of Bipartite Graphs

Ron Aharoni, Eli Berger, Maria Chudnovsky, Frédéric Havet, Zilin Jiang
2020 Electronic Journal of Combinatorics  
of bipartite graphs.  ...  Given a system $(G_1, \ldots ,G_m)$ of graphs on the same vertex set $V$, a cooperative coloring is a choice of vertex sets $I_1, \ldots ,I_m$, such that $I_j$ is independent in $G_j$ and $\bigcup_{j=1  ...  The rest of the paper is organized as follows. In Section 2 and Section 3, we prove Theorem 4 for trees and bipartite graphs respectively.  ... 
doi:10.37236/8111 fatcat:jqvzm4lg7bbvnpufuk432oxnpi


2009 Discrete Applied Mathematics  
Raspaud and W. Wang Injective coloring of planar graphs 663 S. Tazari and M.  ...  Monnot and V.Th. Paschos Weighted coloring on planar, bipartite and split graphs: Complexity and approximation 819 M.R. Darafsheh Groups with the same non-commuting graph 833 H.R.  ... 
doi:10.1016/s0166-218x(09)00028-6 fatcat:w7lrdwnmnjcq5jbjodhopm74ki

Page 4037 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
free crossing graph if and only if G is a cube-free median graph; and (iv) G# is a complete bipartite graph if and only if G is the Cartesian product of two trees.  ...  4037 edge-color a bipartite graph with n nodes, m edges, and maximum degree A.” 2003f:05098 05C75 Hempel, Harald (D-FSUMI,; Jena); Kratsch, Dieter (D-FSUMI; Jena) On claw-free asteroidal triple-free graphs  ... 

Monochromatic and Heterochromatic Subgraphs in Edge-Colored Graphs - A Survey

Mikio Kano, Xueliang Li
2008 Graphs and Combinatorics  
Nowadays the term monochromatic and heterochromatic (or rainbow, multicolored) subgraphs of an edge colored graph appeared frequently in literature, and many results on this topic have been obtained.  ...  There are also some interesting results on vertex-colored graphs, but we do not contain them, either.  ...  However, for complete bipartite graphs, Chen, Jin, Li and Tu [21] gave an explicit formula for the heterochromatic tree partition number of an r-edge colored complete bipartite graph K m,n .  ... 
doi:10.1007/s00373-008-0789-5 fatcat:a4j64ccspze2td7cv3f247kf7u

Mixed graph edge coloring

Hanna Furmańczyk, Adrian Kosowski, Bernard Ries, Paweł Żyliński
2009 Discrete Mathematics  
In particular, we provide N Pcompleteness results for the case of outerplanar graphs, as well as for 3-regular bipartite graphs (even when only 3 colors are allowed, or when 5 colors are allowed and the  ...  In this paper we give general bounds on the number of required colors and analyze the complexity status of this problem.  ...  In [4] [5] [6] polynomial algorithms are given for the cases of mixed trees and mixed series-parallel graphs.  ... 
doi:10.1016/j.disc.2008.11.033 fatcat:cxei7a7u6jf7raoeblkjpm3eiu

Graph-Theoretic Problems and Their New Applications

Frank Werner
2020 Mathematics  
Graph theory is an important area of Applied Mathematics with a broad spectrum of applications in many fields [...]  ...  My special thanks go to the staff of the journal Mathematics for the good and pleasant cooperation during the preparation of this issue.  ...  Conflicts of Interest: The author declares no conflict of interest.  ... 
doi:10.3390/math8030445 fatcat:wrhd55t4png4dj6jw6y5b2bgne

b-coloring of tight graphs

Frédéric Havet, Cláudia Linhares Sales, Leonardo Sampaio
2012 Discrete Applied Mathematics  
We also generalize the concept of pivoted tree introduced by Irving and Manlove (1999) [13] and show its relation with the b-chromatic number of tight graphs.  ...  This characterization is used to propose polynomial-time algorithms for deciding whether χ b (G) = m(G) for tight graphs that are complement of bipartite graphs, P 4 -sparse and block graphs.  ...  The third author was partially supported by CAPES/Brazil and ANR Blanc AGAPE.  ... 
doi:10.1016/j.dam.2011.10.017 fatcat:os34felcmrcuhavh5r34orlu6u

Mixed Graph Colorings: A Historical Review

Yuri N. Sotskov
2020 Mathematics  
Two types of colorings of the vertices of the mixed graph and one coloring of the arcs and edges of the mixed graph have been considered in the literature.  ...  A mixed graph contains both a set of arcs and a set of edges.  ...  In [33] , it was proven that the problem PrExt(G, 2) is polynomially solvable for a bipartite graph G = (V, ∅, E), for a split graph G, and for a complement G of the bipartite graph.  ... 
doi:10.3390/math8030385 fatcat:hp6huli6lvah3dwevm2xr3jefy

Page 7229 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
bipartite graphs.  ...  Given any such graph G({n],£) and any k-bounded coloring of G, the authors find a multicolored set of edges E; UE>.  ... 


2000 Discrete Mathematics  
., The Terwilliger algebra of an almost-bipartite distance-regular graph and its antipodal 2-cover (1}3) 35} 69 CorteH s, C. and A.  ...  |uczak, Embedding trees into graphs of large girth (Note) ( 1 }3) 273}278 Haynes, T.W., see X. Baogen (1}3) 1} 10 Hedetniemi, S.T., see X.  ... 
doi:10.1016/s0012-365x(00)00073-x fatcat:yov7ip52wfe3dbjvwfehnr422u

Stability of Special Graph Classes [article]

Robin Weishaupt, Jörg Rothe
2021 arXiv   pre-print
, bipartite graphs, and co-graphs.  ...  We follow their approach and provide a large number of polynomial-time algorithms solving these problems for special graph classes, namely for graphs without edges, complete graphs, paths, trees, forests  ...  Acknowledgments This work was supported in part by Deutsche Forschungsgemeinschaft under grants RO 1202/14-2 and RO 1202/21-1.  ... 
arXiv:2106.01496v1 fatcat:2l6xdgjksvhsnh3ntm5vnqintm

Author index

2002 Discrete Mathematics  
Cooper and M. Hirschhorn, Relations between squares and triangles (Note) (1}3) 245}247 BollobaH sSchelp, Random induced graphs (Note) ( 1 }3) 249}254 Casse, R. and C.T.  ...  Tomasik, Essential arities in algebras of "nite type and arity trees (1}3) 79} 91 Kwak, J.H. and S.H. Shim, Total embedding distributions for bouquets of circles Pikhurko, O. and A.  ... 
doi:10.1016/s0012-365x(02)00243-1 fatcat:cayjbuxgp5amvpb5wpbk3gsgai

Fair Maximal Independent Sets

Jeremy T. Fineman, Calvin Newport, Micah Sherr, Tonghe Wang
2014 2014 IEEE 28th International Parallel and Distributed Processing Symposium  
colored with a small number of colors.  ...  In this paper, we seek efficient and fair algorithms for common graph families. We begin by describing an algorithm that is fair and runs in O(log * n)-time in rooted trees of size n.  ...  Here we tackle this challenge for T ⊂ B, where T is the class of unrooted trees, and we generalize to bipartite graphs in Section VI, albeit at the cost of a slower algorithm.  ... 
doi:10.1109/ipdps.2014.79 dblp:conf/ipps/FinemanNSW14 fatcat:jrzpdlzew5bb5byt4majv7jlz4

CommGram: A New Visual Analytics Tool for Large Communication Trace Data

Jieting Wu, Jianping Zeng, Hongfeng Yu, Joseph P. Kenny
2014 2014 First Workshop on Visual Performance Analysis  
With the benefit of MPI trace library DUMPI of SST, our framework builds hierarchical clustering trees for computational community domain, and takes advantage of graphical user interface (GUI) to convey  ...  This algorithm exchanges the messages among the processors in a 2-3 tree manner, and the message number is bounded by O(N log N) for N processors.  ...  With the cluster tree, we can begin with a few number of clusters to perceive an overview as the color and size of polygons can provide a high-level visual description of communication among the communities  ... 
doi:10.1109/vpa.2014.8 dblp:conf/sc/WuZYK14 fatcat:it7cuqhfrrgvddpz6ytyu46plu
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