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91.
《Discrete Mathematics》2023,346(1):113188
In this addendum we give a short and easy negative answer to the two questions raised in the original article. 相似文献
92.
93.
On Clique-Transversals and Clique-Independent Sets 总被引:1,自引:0,他引:1
Guillermo Durán Min Chih Lin Jayme L. Szwarcfiter 《Annals of Operations Research》2002,116(1-4):71-77
A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. A clique-independent set is a subset of pairwise disjoint cliques of G. Denote by
C
(G) and
C
(G) the cardinalities of the minimum clique-transversal and maximum clique-independent set of G, respectively. Say that G is clique-perfect when
C
(H)=
C
(H), for every induced subgraph H of G. In this paper, we prove that every graph not containing a 4-wheel nor a 3-fan as induced subgraphs and such that every odd cycle of length greater than 3 has a short chord is clique-perfect. The proof leads to polynomial time algorithms for finding the parameters
C
(G) and
C
(G), for graphs belonging to this class. In addition, we prove that to decide whether or not a given subset of vertices of a graph is a clique-transversal is Co-NP-Complete. The complexity of this problem has been mentioned as unknown in the literature. Finally, we describe a family of highly clique-imperfect graphs, that is, a family of graphs G whose difference
C
(G)–
C
(G) is arbitrarily large. 相似文献
94.
Based on our analysis of the hopcount of the shortest path between two arbitrary nodes in the class G
p
(N) of random graphs, the corresponding flooding time is investigated. The flooding time T
N
(p) is the minimum time needed to reach all other nodes from one node. We show that, after scaling, the flooding time T
N
(p) converges in distribution to the two-fold convolution (2*) of the Gumbel distribution function (z)=exp (–e
–z
), when the link density p
N
satisfies Np
N
/(log N)3 if N . 相似文献
95.
Within the Feynman–Kac path integral representation, the equilibrium quantities of a quantum plasma can be represented by Mayer graphs. The well known Coulomb divergencies that appear in these series are eliminated by partial resummations. In this paper, we propose a resummation scheme based on the introduction of a single effective potential that is the quantum analog of the Debye potential. A low density analysis of shows that it reduces, at short distances, to the bare Coulomb interaction between the charges (which is able to lead to bound states). At scale of the order of the Debye screening length
–1
D, approaches the classical Debye potential and, at large distances, it decays as a dipolar potential (this large distance behaviour is due to the quantum nature of the particles). The prototype graphs that result from the resummation obey the same diagrammatical rules as the classical graphs of the Abe–Meeron series. We give several applications that show the usefulness of to account for Coulombic effects at all distances in a coherent way. 相似文献
96.
本文给出了一个图为Menger型的一个充分必要条件,利用这个条件,我们拓广了已知的Menger型图的类。 相似文献
97.
The accumulation of the Jacobian matrix F of a vector function can be regarded as a transformation of its linearized computational graph into a subgraph of the directed complete bipartite graph Kn,m. This transformation can be performed by applying different elimination techniques that may lead to varying costs for computing F. This paper introduces face elimination as the basic technique for accumulating Jacobian matrices by using a minimal number of arithmetic operations. Its superiority over both edge and vertex elimination methods is shown. The intention is to establish the conceptual basis for the ongoing development of algorithms for optimizing the computation of Jacobian matrices. 相似文献
98.
We solve a problem proposed by Jacobson, Kézdy, and Lehel [4] concerning the existence of forbidden induced subgraph characterizations of line graphs of linear k-uniform hypergraphs with sufficiently large minimal edge-degree. Actually, we prove that for each k3 there is a finite set Z(k) of graphs such that each graph G with minimum edge-degree at least 2k2–3k+1 is the line graph of a linear k-uniform hypergraph if and only if G is a Z(k)-free graph.Acknowledgments. We thank the anonymous referees, whose suggestions helped to improve the presentation of the paper.Winter 2002/2003 DIMACS Award is gratefully acknowledged2000 Mathematics Subject Classification: 05C65 (05C75, 05C85) 相似文献
99.
Let F be a graph of order at most k. We prove that for any integer g there is a graph G of girth at least g and of maximum degree at most 5k13 such that G admits a surjective homomorphism c to F, and moreover, for any F-pointed graph H with at most k vertices, and for any homomorphism h from G to H there is a unique homomorphism f from F to H such that h=fc. As a consequence, we prove that if H is a projective graph of order k, then for any finite family of prescribed mappings from a set X to V(H) (with ||=t), there is a graph G of arbitrary large girth and of maximum degree at most 5k26mt (where m=|X|) such that and up to an automorphism of H, there are exactly t homomorphisms from G to H, each of which is an extension of an f.Supported in part by the National Science Council under grant NSC89-2115-M-110-012Final version received: June 9, 2003 相似文献
100.
Let be a class of graphs on n vertices. For an integer c, let be the smallest integer such that if G is a graph in with more than edges, then G contains a cycle of length more than c. A classical result of Erdös and Gallai is that if is the class of all simple graphs on n vertices, then . The result is best possible when n-1 is divisible by c-1, in view of the graph consisting of copies of Kc all having exactly one vertex in common. Woodall improved the result by giving best possible bounds for the remaining cases when n-1 is not divisible by c-1, and conjectured that if is the class of all 2-connected simple graphs on n vertices, thenwhere , 2tc/2, is the number of edges in the graph obtained from Kc+1-t by adding n-(c+1-t) isolated vertices each joined to the same t vertices of Kc+1-t. By using a result of Woodall together with an edge-switching technique, we confirm Woodall's conjecture in this paper. 相似文献