{"title":"Adjacent vertex strongly distinguishing total coloring of graphs with lower average degree","authors":"Fei Wen, Li Zhou, Zepeng Li","doi":"10.7151/dmgt.2518","DOIUrl":"https://doi.org/10.7151/dmgt.2518","url":null,"abstract":"","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135700693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shariefuddin Pirzada, Saleem Khan, Francesco Belardo
{"title":"On the distribution of distance signless Laplacian eigenvalues with given independence and chromatic number","authors":"Shariefuddin Pirzada, Saleem Khan, Francesco Belardo","doi":"10.7151/dmgt.2524","DOIUrl":"https://doi.org/10.7151/dmgt.2524","url":null,"abstract":"","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135057583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we consider a game played on the edge set of the infinite clique $K_mathbb{N}$ by two players, Builder and Painter. In each round of the game, Builder chooses an edge and Painter colors it red or blue. Builder wins when Painter creates a red copy of $G$ or a blue copy of $H$, for some fixed graphs $G$ and $H$. Builder wants to win in as few rounds as possible, and Painter wants to delay Builder for as many rounds as possible. The online size Ramsey number $tilde{r}(G,H)$, is the minimum number of rounds within which Builder can win, assuming both players play optimally. So far it has been proven by Dybizba'nski, Dzido and Zakrzewska that $11leqtilde{r}(C_4,P_6)leq13$ cite{Dzido}. In this paper, we refine this result and show the exact value, namely we will present the Theorem that $tilde{r}(C_4,P_6)=11$, with the details of the proof. Keywords: graph theory, Ramsey theory, combinatorial games, online size Ramsey number
{"title":"Online size Ramsey number for <i>C<sub>4</sub></i> and <i>P<sub>6</sub></i>","authors":"Mateusz Litka","doi":"10.7151/dmgt.2513","DOIUrl":"https://doi.org/10.7151/dmgt.2513","url":null,"abstract":"In this paper we consider a game played on the edge set of the infinite clique $K_mathbb{N}$ by two players, Builder and Painter. In each round of the game, Builder chooses an edge and Painter colors it red or blue. Builder wins when Painter creates a red copy of $G$ or a blue copy of $H$, for some fixed graphs $G$ and $H$. Builder wants to win in as few rounds as possible, and Painter wants to delay Builder for as many rounds as possible. The online size Ramsey number $tilde{r}(G,H)$, is the minimum number of rounds within which Builder can win, assuming both players play optimally. So far it has been proven by Dybizba'nski, Dzido and Zakrzewska that $11leqtilde{r}(C_4,P_6)leq13$ cite{Dzido}. In this paper, we refine this result and show the exact value, namely we will present the Theorem that $tilde{r}(C_4,P_6)=11$, with the details of the proof. Keywords: graph theory, Ramsey theory, combinatorial games, online size Ramsey number","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135442103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Critical aspects in broadcast domination","authors":"Jishnu Sen, S. Kola","doi":"10.7151/dmgt.2506","DOIUrl":"https://doi.org/10.7151/dmgt.2506","url":null,"abstract":"","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71129976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The tree-achieving set and non-separating independent set problem of subcubic graphs","authors":"Fayun Cao, Han Ren","doi":"10.7151/dmgt.2522","DOIUrl":"https://doi.org/10.7151/dmgt.2522","url":null,"abstract":"","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136301686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The maximum number of edges in a <i>{K<sub>r+1</sub>,M<sub>k+1</sub>}</i>-free graph","authors":"Lingting Fu, Jian Wang, Weihua Yang","doi":"10.7151/dmgt.2515","DOIUrl":"https://doi.org/10.7151/dmgt.2515","url":null,"abstract":"","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135556670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let G be a graph and S ⊆ V (G) represent a subset of vertices having installed “detectors,” each of which is capable of sensing an “intruder” in its open-neighborhood. The open-locating-code of v ∈ V (G) is the set of neighboring detectors, N(v) ∩ S. The set S is said to be an open-locatingdominating set if every open-locating-code is unique and non-empty. In this paper we focus on error-detecting open-locating-dominating sets on the infinite triangular grid, present a solution with density 12 , and prove it is optimal.
{"title":"Optimal error-detecting open-locating-dominating set on the infinite triangular grid","authors":"Devin C. Jean, S. Seo","doi":"10.7151/dmgt.2374","DOIUrl":"https://doi.org/10.7151/dmgt.2374","url":null,"abstract":"Let G be a graph and S ⊆ V (G) represent a subset of vertices having installed “detectors,” each of which is capable of sensing an “intruder” in its open-neighborhood. The open-locating-code of v ∈ V (G) is the set of neighboring detectors, N(v) ∩ S. The set S is said to be an open-locatingdominating set if every open-locating-code is unique and non-empty. In this paper we focus on error-detecting open-locating-dominating sets on the infinite triangular grid, present a solution with density 12 , and prove it is optimal.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88299040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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