图的惟一列表可着色性Кn2 + Kr

IF 0.2 Q4 MATHEMATICS, APPLIED

Prikladnaya Diskretnaya Matematika Pub Date : 2022-01-01 DOI:10.17223/20710410/55/6

L. X. Hung

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引用次数: 0

摘要

给定每个顶点v的列表L(v)，如果存在G的适当顶点着色，其中每个顶点v从L(v)取其颜色，则我们说图G是L可着色的。如果有一个列表赋值L使得|L(v) | = k对于每个顶点v这个图恰好有一个L-着色，那么这个图是唯一的k-列表可着色的。如果一个图G不是唯一的k-list可着色的，我们也说G具有性质M(k)。使G具有M(k)性质的最小整数k称为G的M数，记为M(G)。本文刻画了图G = Kn2 + Kr的唯一表可色性，特别是确定了图G = Kn2 + Kr的个数m(G)。

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Unique list colorability of the graph Кn2 + Kr

Given a list L(v) for each vertex v, we say that the graph G is L-colorable if there is a proper vertex coloring of G, where each vertex v takes its color from L(v). The graph is uniquely k-list colorable if there is a list assignment L such that |L(v) | = k for every vertex v and the graph has exactly one L-coloring with these lists. If a graph G is not uniquely k-list colorable, we also say that G has property M(k). The least integer k such that G has the property M(k) is called the m-number of G, denoted by m(G). In this paper, we characterize the unique list colorability of the graph G = Kn2 + Kr. In particular, we determine the number m(G) of the graph G = Kn2 + Kr.

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来源期刊

Prikladnaya Diskretnaya Matematika MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

50.00%

发文量

期刊介绍： The scientific journal Prikladnaya Diskretnaya Matematika has been issued since 2008. It was registered by Federal Control Service in the Sphere of Communications and Mass Media (Registration Witness PI № FS 77-33762 in October 16th, in 2008). Prikladnaya Diskretnaya Matematika has been selected for coverage in Clarivate Analytics products and services. It is indexed and abstracted in SCOPUS and WoS Core Collection (Emerging Sources Citation Index). The journal is a quarterly. All the papers to be published in it are obligatorily verified by one or two specialists. The publication in the journal is free of charge and may be in Russian or in English. The topics of the journal are the following: 1.theoretical foundations of applied discrete mathematics – algebraic structures, discrete functions, combinatorial analysis, number theory, mathematical logic, information theory, systems of equations over finite fields and rings; 2.mathematical methods in cryptography – synthesis of cryptosystems, methods for cryptanalysis, pseudorandom generators, appreciation of cryptosystem security, cryptographic protocols, mathematical methods in quantum cryptography; 3.mathematical methods in steganography – synthesis of steganosystems, methods for steganoanalysis, appreciation of steganosystem security; 4.mathematical foundations of computer security – mathematical models for computer system security, mathematical methods for the analysis of the computer system security, mathematical methods for the synthesis of protected computer systems;[...]