{"title":"基于可加性质的图多项式弱区分","authors":"J. Makowsky, Vsevolod Rakita","doi":"10.2140/moscow.2020.9.333","DOIUrl":null,"url":null,"abstract":"A graph polynomial $P$ is weakly distinguishing if for almost all finite graphs $G$ there is a finite graph $H$ that is not isomorphic to $G$ with $P(G)=P(H)$. It is weakly distinguishing on a graph property $\\mathcal{C}$ if for almost all finite graphs $G\\in\\mathcal{C}$ there is $H \\in \\mathcal{C}$ that is not isomorphic to $G$ with $P(G)=P(H)$. We give sufficient conditions on a graph property $\\mathcal{C}$ for the characteristic, clique, independence, matching, and domination and $\\xi$ polynomials, as well as the Tutte polynomial and its specialisations, to be weakly distinguishing on $\\mathcal{C}$. One such condition is to be addable and small in the sense of C. McDiarmid, A. Steger and D. Welsh (2005). Another one is to be of genus at most $k$.","PeriodicalId":8442,"journal":{"name":"arXiv: Combinatorics","volume":"50 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Weakly distinguishing graph polynomials on addable properties\",\"authors\":\"J. Makowsky, Vsevolod Rakita\",\"doi\":\"10.2140/moscow.2020.9.333\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A graph polynomial $P$ is weakly distinguishing if for almost all finite graphs $G$ there is a finite graph $H$ that is not isomorphic to $G$ with $P(G)=P(H)$. It is weakly distinguishing on a graph property $\\\\mathcal{C}$ if for almost all finite graphs $G\\\\in\\\\mathcal{C}$ there is $H \\\\in \\\\mathcal{C}$ that is not isomorphic to $G$ with $P(G)=P(H)$. We give sufficient conditions on a graph property $\\\\mathcal{C}$ for the characteristic, clique, independence, matching, and domination and $\\\\xi$ polynomials, as well as the Tutte polynomial and its specialisations, to be weakly distinguishing on $\\\\mathcal{C}$. One such condition is to be addable and small in the sense of C. McDiarmid, A. Steger and D. Welsh (2005). Another one is to be of genus at most $k$.\",\"PeriodicalId\":8442,\"journal\":{\"name\":\"arXiv: Combinatorics\",\"volume\":\"50 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-10-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/moscow.2020.9.333\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/moscow.2020.9.333","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
对于几乎所有有限图$G$,一个图多项式$P$是弱区分是否有一个有限图$H$不同构于$G$且$P(G)=P(H)$。对于几乎所有的有限图$G\in\mathcal{C}$存在$H \in\mathcal{C}$不同构于$G$且$P(G)=P(H)$,这是弱区分图性质$\mathcal{C}$的。给出了图性质$\mathcal{C}$上特征、团、独立、匹配、支配和$\xi$多项式以及Tutte多项式及其专门化在$\mathcal{C}$上弱区分的充分条件。其中一个条件是C. McDiarmid, A. Steger和D. Welsh(2005)意义上的可添加和小。另一种是最多有$k$属。
Weakly distinguishing graph polynomials on addable properties
A graph polynomial $P$ is weakly distinguishing if for almost all finite graphs $G$ there is a finite graph $H$ that is not isomorphic to $G$ with $P(G)=P(H)$. It is weakly distinguishing on a graph property $\mathcal{C}$ if for almost all finite graphs $G\in\mathcal{C}$ there is $H \in \mathcal{C}$ that is not isomorphic to $G$ with $P(G)=P(H)$. We give sufficient conditions on a graph property $\mathcal{C}$ for the characteristic, clique, independence, matching, and domination and $\xi$ polynomials, as well as the Tutte polynomial and its specialisations, to be weakly distinguishing on $\mathcal{C}$. One such condition is to be addable and small in the sense of C. McDiarmid, A. Steger and D. Welsh (2005). Another one is to be of genus at most $k$.