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(i, j) competition graphs

Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J.Richard Lundgren, Fred S. Roberts
1991 Discrete Applied Mathematics  
The next theorem applies not only to (i;J) irredundant competition graphs, but to (i, j) irredundant competition graphs as well.  ...  We say that a graph G is a (u, v) competition graph, where u=i or Tand v =j or j; if it is the competition graph of a (u, v) digraph.  ... 
doi:10.1016/0166-218x(91)90002-e fatcat:wlmw7m6cynce7mv437pxlciemq

Tolerance competition graphs

R.C. Brigham, F.R. McMorris, R.P. Vitray
1995 Linear Algebra and its Applications  
G = (V, E) is a &tolerance competition graph if there is a directed graph D = (V, A) and an assignment of a nonnegative integer ti to each vertex vi E V such that, for i # j, uivj E E(G) if and only if  ...  The r$-tolerance competition graph is introduced as a generalization of the p-competition graphs defined by Kim, McKee, McMorris, and Roberts.  ...  Competition graphs have been studied extensively since being introduced in 1968 by J. 10, 11, 131 .  ... 
doi:10.1016/0024-3795(94)00059-m fatcat:ofz3weze3nb7jpb4n7o7uzvovi

2-Competition Graphs

Garth Isaak, Suh-Ryung Kim, Terry A. McKees, F. R. McMorris, Fred S. Roberts
1992 SIAM Journal on Discrete Mathematics  
In particular, the paper addresses the question of which complete bipartite graphs are 2-competition graphs.  ...  Those who are familiar with the competition graphs literature will note that we do not assume that the digraph D is acyclic, as is often assumed in that literature.  ...  It follows that when j 4: i, then, for any d in C', either c or c' is not in S. We next show that c and c' appear together in at most one S. Case 1. For some j 4: i, cj 4: cj.  ... 
doi:10.1137/0405042 fatcat:5fvjoxynlfc6tkz7xg5ozma5f4

Competitively Tight Graphs

Suh-Ryung Kim, Jung Yeun Lee, Boram Park, Yoshio Sano
2013 Annals of Combinatorics  
Computing the competition number of a graph is an NP-hard problem in general and has been one of the important research problems in the study of competition graphs.  ...  For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph.  ...  Let G be the Cayley graph associated with (Z/nZ, {±1, ±2, . . . , ±p}), i.e., G is the graph defined by V (G) = {v i | i ∈ Z/nZ} and E(G) = {v i v j | ij ∈ {±1, ±2, . . . , ±p}}.  ... 
doi:10.1007/s00026-013-0207-4 fatcat:xrlrxgnpdjbwhfv3gcdecqyaqe

Competitive graph searches

Binh-Minh Bui-Xuan, Michel Habib, Christophe Paul
2008 Theoretical Computer Science  
We exemplify an optimization criterion for divide-and-conquer algorithms with a technique called generic competitive graph search.  ...  For the latter problem, we first study the relationship between the common connected components problem and the cograph sandwich problem, then, using our competitive graph search paradigm, we improve the  ...  We define E such that any pair (x, y) satisfying x ∈ V i , y ∈ V j , and i = j implies (x, y) ∈ E.  ... 
doi:10.1016/j.tcs.2007.10.048 fatcat:q77svt5x5vdj7kzmokdfpxze6u

p-competition graphs

Suh-ryung Kim, Terry A. McKee, F.R. McMorris, Fred S. Roberts
1995 Linear Algebra and its Applications  
This definition generalizes the widely studied p = 1 case of ordinary competition graphs.  ...  We obtain results about pcompetition graphs analogous to the well-known results about ordinary competition graphs and apply these results to specific cases.  ...  in [3, 5, lo] , and the competition multigraph in [I] .  ... 
doi:10.1016/0024-3795(94)00060-q fatcat:zq5rvjjhefdkxobyq6ntkloowe

Price competition on graphs

Pim Heijnen, Adriaan R. Soetevent
2018 Journal of Economic Behavior and Organization  
These graph models of price competition may lead to spatial discontinuities in firm-level demand.  ...  This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs.  ...  A graph G is described by a finite set of nodes N = {1, . . . , n} and a set of edges E ⊂ N × N . Generic elements of N are denoted by i and j. If i and j share an edge, then (i, j) ∈ E.  ... 
doi:10.1016/j.jebo.2017.12.011 fatcat:c3whl54ugvfalh46o5ilqytu7i

Price Competition on Graphs

Pim Heijnen, Adriaan R. Soetevent
2014 Social Science Research Network  
A graph G is described by a finite set of nodes N = {1, . . . , n} and a set of edges E ⊂ N × N . Generic elements of N are denoted by i and j. If i and j share an edge, then (i, j) ∈ E.  ...  • If min{f (x i ), f (x j )} ≥ µ, then ν ij (µ) = 0 • If max{f (x i ), f (x j )} ≤ µ, then ν ij (µ) = ij • Else find the value of t such that f (tx i + (1 − t)x j ) = µ -If f (x i ) ≤ µ, then ν ij (  ... 
doi:10.2139/ssrn.2504454 fatcat:tqubh5d7nreplbsdd52ns6okf4

Price Competition on Graphs

Adriaan R. Soetevent
2010 Social Science Research Network  
A graph G is described by a finite set of nodes N = {1, . . . , n} and a set of edges E ⊂ N × N . Generic elements of N are denoted by i and j. If i and j share an edge, then (i, j) ∈ E.  ...  • If min{f (x i ), f (x j )} ≥ µ, then ν ij (µ) = 0 • If max{f (x i ), f (x j )} ≤ µ, then ν ij (µ) = ij • Else find the value of t such that f (tx i + (1 − t)x j ) = µ -If f (x i ) ≤ µ, then ν ij (  ... 
doi:10.2139/ssrn.1725158 fatcat:xmwicmtkzfaq7mzs5z5ehxv3zq

Competition numbers of planar graphs [article]

Jihoon Choi, Soogang Eoh, Suh-Ryung Kim
2018 arXiv   pre-print
number, the competition number, and the co-competition number of a graph G, respectively.  ...  By utilizing this inequality and a notion of competition-effective edge clique cover, we obtain some meaningful results on competition numbers of planar graphs.  ...  Since A i j ∈ S, N B (A i j ) ⊂ N B (S). Therefore z ∈ N B (S) since z ∈ A i j and A i j = N B (A i j ).  ... 
arXiv:1602.04623v3 fatcat:tdizvab7ynhcnm5s3afcjpota4

Cycles and p-competition graphs [article]

Suh-Ryung Kim, Boram Park, Yoshio Sano
2009 arXiv   pre-print
Roberts [p-competition graphs, Linear Algebra Appl., 217 (1995) 167--178] as a generalization of the competition graphs of digraphs. Let p be a positive integer.  ...  vertices v_1, ..., v_p in V such that (x,v_i), (y,v_i) are arcs of the digraph D for each i=1, ..., p.  ...  (i) For p ≤ 4, C 6 is a p-competition graph. For p ≤ 1, C 7 is a p-competition graph. For p ≤ 5, C 8 is a p-competition graph. (ii) If n ≥ 9 is odd and p ≤ n−3 2 , then C n is a p-competition graph.  ... 
arXiv:0905.3942v1 fatcat:ipjhthblgzf2foonzc2rl2jriu

Competition Graphs of Hamiltonian Digraphs

David R. Guichard
1998 SIAM Journal on Discrete Mathematics  
Fraughnaugh et al. proved that a graph G is the competition graph of a hamiltonian digraph possibly having loops if and only if G has an edge clique cover C = {C 1 , . . . , Cn} that has a system of distinct  ...  [SIAM J. Discrete Math., 8 (1995), pp. 179-185]. We settle a question left open by their work, by showing that the words "possibly having loops" may be removed.  ...  The clique graph CG(C, V) is the digraph whose vertices are the cliques, with arc (C i , C j ) if and only if v j / ∈ C i .  ... 
doi:10.1137/s089548019629735x fatcat:ku62v23eznhpnjwo3rpmk6acqy

Competition graphs induced by permutations [article]

Brian Nakamura, Elizabeth Yang
2015 arXiv   pre-print
In prior work, Cho and Kim studied competition graphs arising from doubly partial orders. In this article, we consider a related problem where competition graphs are instead induced by permutations.  ...  We classify the competition graphs arising from 132-avoiding permutations and show that those graphs must avoid an induced path graph of length 3.  ...  The edge {π i , π j } is in the competition graph C(π) if and only if there exists a π k such that k < i, j and π k < π i , π j , in which case the subsequence π k π i π j forms either a 123 or a 132 pattern  ... 
arXiv:1503.05617v1 fatcat:ykzwvpexxzcefhyevcjezcejg4

Competitive Colorings of Oriented Graphs

H. A. Kierstead, W. T. Trotter
2000 Electronic Journal of Combinatorics  
and ${\cal C}$ does not contain a complete graph on $k$ vertices, then whenever $G$ is an orientation of a graph from ${\cal C}$, the oriented game chromatic number of $G$ is at most $t$.  ...  In particular, oriented planar graphs have bounded oriented game chromatic number. This answers a question raised by Nešetřil and Sopena.  ...  Next, we describe how the labels assigned to the vertices in C i are used to determine the random graph H i . Start with the graph G. Then let x j ∈ C i .  ... 
doi:10.37236/1611 fatcat:fhlokol7e5cgxid5bazyp4p7oq

Certain Bipolar Neutrosophic Competition Graphs

Muhammad Akram
2017 Journal of the Indonesian Mathematical Society  
competition graphs.  ...  In this paper, we first introduce the concept of p-competition bipo-lar neutrosophic graphs.  ...  a i ), q P i = − → J (x, a i ) ∧ − → J (y, a i ), q N i = − → J (x, a i ) ∨ − → J (y, a i ), r P i = − → J (x, a i ) ∨ − → J (y, a i ), r N i = − → J (x, a i ) ∧ − → J (y, a i ).  ... 
doi:10.22342/jims.24.1.455.1-25 fatcat:qeotklupdzgoze4z7i7cmb6eky
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