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(i, j) competition graphs

1991
*
Discrete Applied Mathematics
*

The next theorem applies not only to (

doi:10.1016/0166-218x(91)90002-e
fatcat:wlmw7m6cynce7mv437pxlciemq
*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. ...##
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Tolerance competition graphs

1995
*
Linear Algebra and its Applications
*

G = (V, E) is a &tolerance

doi:10.1016/0024-3795(94)00059-m
fatcat:ofz3weze3nb7jpb4n7o7uzvovi
*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 . ...##
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2-Competition Graphs

1992
*
SIAM Journal on Discrete Mathematics
*

In particular, the paper addresses the question of which complete bipartite

doi:10.1137/0405042
fatcat:5fvjoxynlfc6tkz7xg5ozma5f4
*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. ...##
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Competitively Tight Graphs

2013
*
Annals of Combinatorics
*

Computing the

doi:10.1007/s00026-013-0207-4
fatcat:xrlrxgnpdjbwhfv3gcdecqyaqe
*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*|*i*−*j*∈ {±1, ±2, . . . , ±p}}. ...##
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Competitive graph searches

2008
*
Theoretical Computer Science
*

We exemplify an optimization criterion for divide-and-conquer algorithms with a technique called generic

doi:10.1016/j.tcs.2007.10.048
fatcat:q77svt5x5vdj7kzmokdfpxze6u
*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. ...##
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p-competition graphs

1995
*
Linear Algebra and its Applications
*

This definition generalizes the widely studied p = 1 case of ordinary

doi:10.1016/0024-3795(94)00060-q
fatcat:zq5rvjjhefdkxobyq6ntkloowe
*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*] . ...##
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Price competition on graphs

2018
*
Journal of Economic Behavior and Organization
*

These

doi:10.1016/j.jebo.2017.12.011
fatcat:c3whl54ugvfalh46o5ilqytu7i
*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. ...##
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Price Competition on Graphs

2014
*
Social Science Research Network
*

A

doi:10.2139/ssrn.2504454
fatcat:tqubh5d7nreplbsdd52ns6okf4
*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 ( ...##
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Price Competition on Graphs

2010
*
Social Science Research Network
*

A

doi:10.2139/ssrn.1725158
fatcat:xmwicmtkzfaq7mzs5z5ehxv3zq
*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 ( ...##
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Competition numbers of planar graphs
[article]

2018
*
arXiv
*
pre-print

number, the

arXiv:1602.04623v3
fatcat:tdizvab7ynhcnm5s3afcjpota4
*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*). ...##
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Cycles and p-competition graphs
[article]

2009
*
arXiv
*
pre-print

Roberts [p-

arXiv:0905.3942v1
fatcat:ipjhthblgzf2foonzc2rl2jriu
*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*. ...##
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Competition Graphs of Hamiltonian Digraphs

1998
*
SIAM Journal on Discrete Mathematics
*

Fraughnaugh et al. proved that a

doi:10.1137/s089548019629735x
fatcat:ku62v23eznhpnjwo3rpmk6acqy
*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*. ...##
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Competition graphs induced by permutations
[article]

2015
*
arXiv
*
pre-print

In prior work, Cho and Kim studied

arXiv:1503.05617v1
fatcat:ykzwvpexxzcefhyevcjezcejg4
*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 ...##
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Competitive Colorings of Oriented Graphs

2000
*
Electronic Journal of Combinatorics
*

and ${\cal C}$ does not contain a complete

doi:10.37236/1611
fatcat:fhlokol7e5cgxid5bazyp4p7oq
*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*. ...##
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Certain Bipolar Neutrosophic Competition Graphs

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*). ...

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