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P3-isomorphisms for graphs

1997
*
Journal of Graph Theory
*

P 3 -

doi:10.1002/(sici)1097-0118(199709)26:1<35::aid-jgt5>3.0.co;2-i
fatcat:ndfyozwnrvhe3epm3bewori4yu
*ISOMORPHISMS**FOR**GRAPHS*37 THORNS, DIAMONDS, SWAPS AND DISCONNECTED*GRAPHS*In this section we establish much of the necessary terminology*for*our work. ... We also characterize all*isomorphisms*between P 3 -*graphs*in terms of the original*graphs*. ... In Section 2, we discuss some basic constructions*for*noninduced P 3 -*isomorphisms*and the situation*for*disconnected*graphs*. ...##
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The generation of minimal triangle graphs

1967
*
Mathematics of Computation
*

T is a minimal triangle set (MTS) of order n if (i) GiT) has n vertices and is connected, and (ii) G(T -\t) ) satisfies (i)

doi:10.1090/s0025-5718-1967-0223276-1
fatcat:knkb4y5mhfcjblvg2aohkk3adq
*for*no t in T. ... In such a case G(T) is a minimal triangle*graph*(MTG) of order n. Our problem is to generate all (nonisomorphic) MTS's of a given order or equivalently (by Theorem 1) all ... We are left with the problem of sorting out*isomorphic*MTS's.*For*this purpose a routine was developed*for*testing two*graphs**for**isomorphism*(described in the next paragraph ). ...##
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The Generation of Minimal Triangle Graphs

1967
*
Mathematics of Computation
*

T is a minimal triangle set (MTS) of order n if (i) GiT) has n vertices and is connected, and (ii) G(T -\t) ) satisfies (i)

doi:10.2307/2004171
fatcat:flou3hs26bgglhup3xswifx2oi
*for*no t in T. ... In such a case G(T) is a minimal triangle*graph*(MTG) of order n. Our problem is to generate all (nonisomorphic) MTS's of a given order or equivalently (by Theorem 1) all ... We are left with the problem of sorting out*isomorphic*MTS's.*For*this purpose a routine was developed*for*testing two*graphs**for**isomorphism*(described in the next paragraph ). ...##
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Randomly decomposable graphs

1985
*
Discrete Mathematics
*

Ruiz and a rational number a, such that 0 < a ~< 1, does there exist a regular Hdecomposable

doi:10.1016/0012-365x(85)90161-x
fatcat:xkbzgufti5fjpgzcpe54b2sge4
*graph*G*for*which i(G: H)= ~? ... A*graph*G is randomly*P3*-decomposable if and only if each component of G is*isomorphic*to C4 or a star of even size. Proof. ... If G is eulerian, then every two consecutive edges of an eulerian circuit account*for*a copy of*P3*, producing the desired*P3*-decomposition. ...##
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The distance between a graph and its complement

1987
*
Czechoslovak Mathematical Journal
*

If n ^ 4, then P" contains an induced subgraph

doi:10.21136/cmj.1987.102139
fatcat:5rjoykb7kbditcb4nchh3tflbq
*isomorphic*to*P3*; the subgraph induced by the same vertex set in P" is also*isomorphic*to*P3*. The*graph**P3*has four vertices and thus ô{P") g n -4. ... The assertions*for*Pj and P2 are evident. The path*P3*is a self-complementary*graph*. ...##
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Page 12 of Mathematical Reviews Vol. , Issue 2004b
[page]

2004
*
Mathematical Reviews
*

The results include: a characterization of directed

*graphs*D with*P3*(D)*isomorphic*to D; a characterization of directed*graphs*D with*P3*(D) Eulerian or Hamiltonian; and that an*isomorphism*between*P3*(D ... ,) and*P3*(D>) almost always implies an*isomorphism*between D, and D>. ...##
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Stability of cartesian products

1978
*
Journal of combinatorial theory. Series B (Print)
*

Further we show that except

doi:10.1016/0095-8956(78)90002-3
fatcat:jzcfssd7yvdsdbpeagalr6gavy
*for*certain (listed) restricted*graphs*, comected cartesian products are semi-stable at every vertex. ... Finally, we show that the cartesian product of any two*graphs*is not semi-stable if and only if one of them is totally disconnected and the other is not semi-stable. 258 ... But this*graph*is*isomorphic*to M i.e. M g P2 x KT*for*some subgraph M of H. Also, by P7, So in case (a), either we have a contradiction, or w1 is a perturbation point of H. ...##
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Generations of triangulations of the sphere

1967
*
Mathematics of Computation
*

First we develop a method

doi:10.1090/s0025-5718-1967-0223277-3
fatcat:fonppcww7radhhk3fpo3dc67mq
*for*generating all triangulations with JV vertices which may yield several triangulations of the same*isomorphism*type, and then wre describe an*isomorphism*routine*for*eliminating ... The slight complication here is needed to insure that T' is a triangulation;*for*if Pi were adjacent to*P3*in T, then T' would have multiple edges and would not be a triangulation. ... The authors are indebted to the University of California (Berkeley) Computer Center*for*the use of its machines. University of California Berkeley, California 94533 ...##
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Generation of Triangulations of the Sphere

1967
*
Mathematics of Computation
*

First we develop a method

doi:10.2307/2004172
fatcat:m7u7kh2cdbbhninuw2isowkbhm
*for*generating all triangulations with JV vertices which may yield several triangulations of the same*isomorphism*type, and then wre describe an*isomorphism*routine*for*eliminating ... The slight complication here is needed to insure that T' is a triangulation;*for*if Pi were adjacent to*P3*in T, then T' would have multiple edges and would not be a triangulation. ... The authors are indebted to the University of California (Berkeley) Computer Center*for*the use of its machines. University of California Berkeley, California 94533 ...##
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Page 2095 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

They also characterize all

*isomorphisms*between*P3*-*graphs*in terms of the original*graphs*. ... In the present paper the authors show that connected finite simple*graphs*G and H with*isomorphic**P3*-*graphs*are either*isomorphic*or part of three exceptional families. ...##
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Some perfect coloring properties of graphs

1979
*
Journal of combinatorial theory. Series B (Print)
*

*For*any

*graph*G, the following statements are equivalent: (5) G is *p-perfect. (6) G is z,bx-perfect. (7) G does not contain an induced subgraph

*isomorphic*to one of the

*graphs*P4 ,

*P3*v P2 or Pz V P2 ... By inspection, one can verify that in any case a subset of these points induce a

*graph*

*isomorphic*to P4 ,

*P3*u P, . or P, u Pz u Pz . ...

##
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ON SMALLEST ORDER OF TRIANGLE-FREE GRAPHS WITH PRESCRIBED (3, k)-DEFECTIVE CHROMATIC NUMBER

2018
*
Far East Journal of Mathematical Sciences (FJMS)
*

We show that f(3, 1) = 9 and characterize the corresponding minimal

doi:10.17654/ms103040717
fatcat:xpznpo5afrge7kb72pq3h7jvli
*graphs*.*For*m ~ 4, we present lower and upper bounds*for*f(m,l). ... The k-defective chromatic number Xk(G) of a*graph*G is the least positive integer m*for*which G is (m,k)-colourable. Let f(m,k) be the smallest order of a triangle-free*graph*G such that X k (G) = m. ...*For*n I and 2 the*graphs*Kl and*P3*, respectively, have the required properties. Assume that R is a triangle-free*graph*of order p with Xl (R) = k, where k :?: 3. ...##
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Page 2273 of Mathematical Reviews Vol. , Issue 85f
[page]

1985
*
Mathematical Reviews
*

A

*graph*is vertex pancyclic if each of its vertices lies on a cycle of length |,*for*each | with 3 <1< |V(G)|. Y is a*graph**isomorphic*to S(K;,3) minus an end vertex.) ... Enomoto and the author [same journal 20 (1981), 117-141; MR 83a:05077], namely (1.1) |E(G)| > jn — 42 holds*for*a*P3*- connected*graph*G with n vertices. ...##
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Page 3936 of Mathematical Reviews Vol. , Issue 96g
[page]

1996
*
Mathematical Reviews
*

Summary: “

*For**graphs*G and G’ with minimum degree at least 3 and satisfying one of three other conditions, we prove that any*isomorphism*from the*P3*-*graph**P3*(G) onto*P3*(G’) can be induced by a (vertex- ... )*isomorphism*of G onto G’. ...##
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The structure of the models of decidable monadic theories of graphs

1991
*
Annals of Pure and Applied Logic
*

., The structure of the models of decidable monadic theories of

doi:10.1016/0168-0072(91)90054-p
fatcat:s2bqebrcyjcyrjubibf2vca3oq
*graphs*, Annals of Pure and Applied Logic 53 (1991) 169-195. ... Let f be an*isomorphism*from Q2,+1 to GA and define &:= {f(e): e E &}*for*i = 1, 2, 3. Now assume that PI,i, P2,i and*P3*,i are already defined*for*an i with 0 < i < 1. ... There was also conjectured a similar results*for*planar*graphs*with no minor*isomorphic*to Q, (*for*n 2 3). This results holds also*for*infinite'*graphs*G. Theorem 2 (Thomas [70, 73] ). ...
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