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Maximum w-cyclic holey group divisible packings and their application to three-dimensional optical orthogonal codes 最大w循环空穴群可分填料及其在三维光学正交码中的应用
SIAM J. Discret. Math. Pub Date : 2022-04-01 DOI: 10.1016/j.disc.2021.112754
Zenghui Fang, Junling Zhou, Lidong Wang
{"title":"Maximum w-cyclic holey group divisible packings and their application to three-dimensional optical orthogonal codes","authors":"Zenghui Fang, Junling Zhou, Lidong Wang","doi":"10.1016/j.disc.2021.112754","DOIUrl":"https://doi.org/10.1016/j.disc.2021.112754","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87668718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Extremal augmented Zagreb index of trees with given numbers of vertices and leaves 给定顶点数和叶子数的树的极值增广萨格勒布指数
SIAM J. Discret. Math. Pub Date : 2022-04-01 DOI: 10.1016/j.disc.2021.112753
Chaohui Chen, Muhuo Liu, Xiaofeng Gu, K. Das
{"title":"Extremal augmented Zagreb index of trees with given numbers of vertices and leaves","authors":"Chaohui Chen, Muhuo Liu, Xiaofeng Gu, K. Das","doi":"10.1016/j.disc.2021.112753","DOIUrl":"https://doi.org/10.1016/j.disc.2021.112753","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72709846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Nonexistence of linear codes meeting the Griesmer bound 不存在满足Griesmer界的线性码
SIAM J. Discret. Math. Pub Date : 2022-04-01 DOI: 10.1016/j.disc.2021.112744
W. Ma, Jinquan Luo
{"title":"Nonexistence of linear codes meeting the Griesmer bound","authors":"W. Ma, Jinquan Luo","doi":"10.1016/j.disc.2021.112744","DOIUrl":"https://doi.org/10.1016/j.disc.2021.112744","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72844079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Spectrum of Triangle-Free Graphs 无三角图的谱
SIAM J. Discret. Math. Pub Date : 2022-03-31 DOI: 10.1137/22m150767x
J. Balogh, F. Clemen, Bernard Lidick'y, S. Norin, Jan Volec
{"title":"The Spectrum of Triangle-Free Graphs","authors":"J. Balogh, F. Clemen, Bernard Lidick'y, S. Norin, Jan Volec","doi":"10.1137/22m150767x","DOIUrl":"https://doi.org/10.1137/22m150767x","url":null,"abstract":"Denote by $q_n(G)$ the smallest eigenvalue of the signless Laplacian matrix of an $n$-vertex graph $G$. Brandt conjectured in 1997 that for regular triangle-free graphs $q_n(G) leq frac{4n}{25}$. We prove a stronger result: If $G$ is a triangle-free graph then $q_n(G) leq frac{15n}{94}<frac{4n}{25}$. Brandt's conjecture is a subproblem of two famous conjectures of ErdH{o}s: (1) Sparse-Half-Conjecture: Every $n$-vertex triangle-free graph has a subset of vertices of size $lceilfrac{n}{2}rceil$ spanning at most $n^2/50$ edges. (2) Every $n$-vertex triangle-free graph can be made bipartite by removing at most $n^2/25$ edges. In our proof we use linear algebraic methods to upper bound $q_n(G)$ by the ratio between the number of induced paths with 3 and 4 vertices. We give an upper bound on this ratio via the method of flag algebras.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77250556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Saturation of Ordered Graphs 有序图的饱和
SIAM J. Discret. Math. Pub Date : 2022-03-10 DOI: 10.1137/22m1485735
V. Boskovic, Balázs Keszegh
{"title":"Saturation of Ordered Graphs","authors":"V. Boskovic, Balázs Keszegh","doi":"10.1137/22m1485735","DOIUrl":"https://doi.org/10.1137/22m1485735","url":null,"abstract":"Recently, the saturation problem of $0$-$1$ matrices gained a lot of attention. This problem can be regarded as a saturation problem of ordered bipartite graphs. Motivated by this, we initiate the study of the saturation problem of ordered and cyclically ordered graphs. We prove that dichotomy holds also in these two cases, i.e., for a (cyclically) ordered graph its saturation function is either bounded or linear. We also determine the order of magnitude for large classes of (cyclically) ordered graphs, giving infinite many examples exhibiting both possible behaviours, answering a problem of P'alv\"olgyi. In particular, in the ordered case we define a natural subclass of ordered matchings, the class of linked matchings, and we start their systematic study, concentrating on linked matchings with at most three links and prove that many of them have bounded saturation function. In both the ordered and cyclically ordered case we also consider the semisaturation problem, where dichotomy holds as well and we can even fully characterize the graphs that have bounded semisaturation function.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85319272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-Colorings of Normed Spaces without Long Monochromatic Unit Arithmetic Progressions 无长单色单位等差列赋范空间的双着色
SIAM J. Discret. Math. Pub Date : 2022-03-09 DOI: 10.1137/22M1483700
V. Kirova, A. Sagdeev
{"title":"Two-Colorings of Normed Spaces without Long Monochromatic Unit Arithmetic Progressions","authors":"V. Kirova, A. Sagdeev","doi":"10.1137/22M1483700","DOIUrl":"https://doi.org/10.1137/22M1483700","url":null,"abstract":"Given a natural $n$, we construct a two-coloring of $mathbb{R}^n$ with the maximum metric satisfying the following. For any finite set of reals $S$ with diameter greater than $5^{n}$ such that the distance between any two consecutive points of $S$ does not exceed one, no isometric copy of $S$ is monochromatic. As a corollary, we prove that any normed space can be two-colored such that all sufficiently long unit arithmetic progressions contain points of both colors.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83338635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The 2-partially distance-regular graphs such that their second largest local eigenvalues are at most one 2-部分距离正则图，其第二大局部特征值最多为1
SIAM J. Discret. Math. Pub Date : 2022-03-01 DOI: 10.1016/j.disc.2021.112749
Yuanjia Zhang, Xiaoye Liang, J. Koolen
{"title":"The 2-partially distance-regular graphs such that their second largest local eigenvalues are at most one","authors":"Yuanjia Zhang, Xiaoye Liang, J. Koolen","doi":"10.1016/j.disc.2021.112749","DOIUrl":"https://doi.org/10.1016/j.disc.2021.112749","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75568106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Signed Langford sequences 有符号兰福德序列
SIAM J. Discret. Math. Pub Date : 2022-03-01 DOI: 10.1016/j.disc.2021.112719
Heather Jordon, Lon H. Mitchell
{"title":"Signed Langford sequences","authors":"Heather Jordon, Lon H. Mitchell","doi":"10.1016/j.disc.2021.112719","DOIUrl":"https://doi.org/10.1016/j.disc.2021.112719","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86254946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characteristic Dependence of Syzygies of Random Monomial Ideals 随机单项式理想合子的特征依赖性
SIAM J. Discret. Math. Pub Date : 2022-03-01 DOI: 10.1137/21m1392474
Caitlyn Booms-Peot, D. Erman, Jay Yang
{"title":"Characteristic Dependence of Syzygies of Random Monomial Ideals","authors":"Caitlyn Booms-Peot, D. Erman, Jay Yang","doi":"10.1137/21m1392474","DOIUrl":"https://doi.org/10.1137/21m1392474","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76887326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Group divisible designs with block size 4 where the group sizes are congruent to 2 mod 3 组可分设计，块大小为4，其中组大小等于2 mod 3
SIAM J. Discret. Math. Pub Date : 2022-03-01 DOI: 10.1016/j.disc.2021.112740
R. Abel, Thomas Britz, Yudhistira A. Bunjamin, Diana Combe
{"title":"Group divisible designs with block size 4 where the group sizes are congruent to 2 mod 3","authors":"R. Abel, Thomas Britz, Yudhistira A. Bunjamin, Diana Combe","doi":"10.1016/j.disc.2021.112740","DOIUrl":"https://doi.org/10.1016/j.disc.2021.112740","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82689748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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