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Highly Irregular m-Chromatic Graphs [chapter]

Yousef Alavi, Fred Buckley, Marc Shamula, Sergio Ruiz
1988 Annals of Discrete Mathematics  
In this paper, we study existence and extremal problems for highly irregular graphs with a given maximum degree and focus our attention on highly irregular graphs that are m-chromatic for m 3 2.  ...  A graph is highly irregular if it is connected and the neighbors of each vertex have distinct degrees.  ...  m-Chromatic graphs Corollary 5 has the following generalization kindly communicated to us by Chartrand. Theorem 6. Let G be a highly irregular m-chromatic A-graph, m 2 3. Then A>2m-2. Proof.  ... 
doi:10.1016/s0167-5060(08)70765-9 fatcat:ktogduiruzdslm2r4p7psrkdga

Highly irregular m-chromatic graphs

Yousef Alavi, Fred Buckley, Marc Shamula, Sergio Ruiz
1988 Discrete Mathematics  
In this paper, we study existence and extremal problems for highly irregular graphs with a given maximum degree and focus our attention on highly irregular graphs that are m-chromatic for m 3 2.  ...  A graph is highly irregular if it is connected and the neighbors of each vertex have distinct degrees.  ...  m-Chromatic graphs Corollary 5 has the following generalization kindly communicated to us by Chartrand. Theorem 6. Let G be a highly irregular m-chromatic A-graph, m 2 3. Then A>2m-2. Proof.  ... 
doi:10.1016/0012-365x(88)90188-4 fatcat:3753b6pjfnh2dez5uppwzt53o4

Page 1382 of Mathematical Reviews Vol. , Issue 90C [page]

1990 Mathematical Reviews  
The paper concludes with a few results on highly irregular m-chromatic graphs. {For the entire collection see MR 89j:05007a.} Ortrud R. Oellermann (1-WM1I)  ...  Alan Tucker (1-SUNYS-S) 90c:05079 O05C15 05C05 05C38 Alavi, Yousef (1-WMI); Buckley, Fred (1-CUNY2); Shamula, Marc (1-CUNY2); Ruiz, Sergio (RCH-UCV) Highly irregular m-chromatic graphs.  ... 

Author index to volume 145 (1995)

1995 Discrete Mathematics  
Lehel, Irregular embeddings of multigraphs with fixed chromatic number (Note) (1 3) 295-299 Jendro'l, S. and M.  ...  -M. and Y. Liu, On the chromatic uniqueness of the graph W(n, n -2) + K k (1--3) 95 103 Gravier, S. and A.  ...  ., Random walks and orthogonal functions associated with highly symmetric graphs  ... 
doi:10.1016/0012-365x(95)90083-w fatcat:vssxfxs7c5a4neq6ixqbnr2j24

Page 774 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
Let G be a highly irregular graph and A(G) its maximum degree. We show that if A(G) > 2, then 77(G) = A(G) +1.  ...  Vijayakumar (Cochin) 99b:05068 05C15 Zhang, Xian Di (PRC-EST-AM; Chengdu) Total colorings of highly irregular graphs of high degree. (Chinese.  ... 

Page 5292 of Mathematical Reviews Vol. , Issue 93j [page]

1993 Mathematical Reviews  
of a graph G.” 93j:05063 05C20 Alavi, Yousef (1-WMI); Liu, Jiu Qiang (1-WMI); Wang, Jian Fang (PRC-ASBJ-AM) Highly irregular digraphs.  ...  In this paper, we investigate some problems concerning the existence of highly irregular digraphs with special properties, with particular focus on highly irregular directed trees as well as their independence  ... 

Author index to volume 164 (1997)

1997 Discrete Mathematics  
Michael, Degree sequences of highly irregular graphs (1-3) 225-236 Majcher, Z. and J. Michael, Highly irregular graphs with extreme numbers of edges , A. and M.  ...  Volkmann, On cycles through a given vertex in multipar-, M. and S. Jendrol, On the d-distance face chromatic number of plane graphs (1-3) 171-174 Jendrol, S., see M.  ... 
doi:10.1016/s0012-365x(97)84783-8 fatcat:vheqou5bfnhuzbok7wzs3b3kfa

Page 4697 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews  
irregular graphs (225-236); Zofia Majcher and Jerzy Michael, Highly irregular graphs with extreme numbers of edges (237-242); Konrad Piwakowski, On Ramsey number R(4, 3,3) and triangle-free edge-chromatic  ...  M. Gutin], Paths and cycles in extended and decomposable digraphs (5-19); Halina Bielak, Chromatic uniqueness in a family of 2-connected graphs (21-28); H. J.  ... 

Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs

Julien Bensmail, Gabriel Renault
2016 Graphs and Combinatorics  
Namely, we prove that every oriented graph can be decomposed into 6 locally irregular oriented graphs.  ...  We say that G is decomposable into k locally irregular graphs if there exists a partition E 1 ∪ E 2 ∪ ... ∪ E k of the edge set E(G) such that each E i induces a locally irregular graph.  ...  [1] , who defined a highly irregular graph as a graph whose every two adjacent vertices have distinct degrees.  ... 
doi:10.1007/s00373-016-1705-z fatcat:prgmt2frmzduhbmucfkwih2hgy

Complexity of determining the irregular chromatic index of a graph [chapter]

Julien Bensmail
2013 The Seventh European Conference on Combinatorics, Graph Theory and Applications  
The irregular chromatic index χ irr (G) of G is the least number of colours used by a locally irregular edge colouring of G (if any).  ...  A graph G is locally irregular if adjacent vertices of G have different degrees.  ...  Locally irregular graphs were first introduced under the name of highly irregular graphs in a work aiming at defining some possible ways for catching the irregularity of graphs [2] .  ... 
doi:10.1007/978-88-7642-475-5_104 fatcat:3ankb7fbxnhlzgdvojnnzx7jaa

New measures of graph irregularity [article]

Clive Elphick, Pawel Wocjan
2014 arXiv   pre-print
In this paper, we define and compare four new measures of graph irregularity. We use these measures to prove upper bounds for the chromatic number and the Colin de Verdiere parameter.  ...  We also strengthen the concise Turan theorem for irregular graphs and investigate to what extent Turan's theorem can be similarly strengthened for generalized r-partite graphs.  ...  The graphs representing some actual networks, such as the World Wide Web, power grids, academic collaborators and neural networks, are highly irregular.  ... 
arXiv:1305.3570v7 fatcat:ghyms4ysjfh6lh53guejtzbtte

Page 5392 of Mathematical Reviews Vol. , Issue 89J [page]

1989 Mathematical Reviews  
ISBN 0-444-70538-4 Contents: Yousef Alavi, Fred Buckley, Marc Shamula and Sergio Ruiz, Highly irregular m-chromatic graphs (pp. 3-13); N. Alon and F. R. K.  ...  Hedetniemi, The edge sub- chromatic number of a graph (pp. 95-104); Ehab S. El-Mallah and Charles J.  ... 

Page 42 of Mathematical Reviews Vol. , Issue 94a [page]

1994 Mathematical Reviews  
if G is an outerplanar graph. X. D. Zhang and others proved that G € C} if G is a highly irregular graph, i.e., for any v € V, d(u) 4 d(w) if vv,uw € E. Let G be a simple graph.  ...  if G is a simple graph (x(G) and x’(G) are the vertex chromatic number and the edge chromatic number, respec- tively).  ... 

Author index to volume

2004 Discrete Mathematics  
Marczyk and M. Wo! zniak, A note on pancyclism of highly connected graphs (1-2) 57-60 Flandrin, E., see M.E.K. Abderrezzak (1-2) 5-13 Fletcher, R.J., C. Koukouvinos and J.  ...  Kemnitz, The circular chromatic index (1-2) 89-93 Ha"uszczak, M., see M.x. Borowiecki (1-2) 37-43 Harant, J., On paths and cycles through specified vertices (1-2) 95-98 Harant, J., see F.  ...  Marczyk and M. Wo! zniak, A note on pancyclism of highly connected graphs , R.J., C. Koukouvinos and J.  ... 
doi:10.1016/s0012-365x(04)00345-0 fatcat:6zribkcwoneppcmbtj3xqfm3qy

Structural Fault Detection In Random Macro Textures

J. Kittler, R. Marik, M. Mirmehdi, M. Petrou
1996 Zenodo  
The placement o f the primitives within these is purely random and highly irregular.  ...  INTRODUCTION Texture is generally divided into two m a i n t ypes: micro and macro textures.  ... 
doi:10.5281/zenodo.36046 fatcat:cv4mklmt3jd45n6c3ucvojjyxy
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