THE ELECTRONIC JOURNAL OF COMBINATORICS (2014), DS1.14 References

and Computing 11. The results of 143 references depend on computer algorithms. The references are ordered alphabetically by the last name of the first author, and where multiple papers have the same first author they are ordered by the last name of the second author, etc. We preferred that all work by the same author be in consecutive positions. Unfortunately, this causes that some of the abbreviations are not in alphabetical order. For example, [BaRT] is earlier on the list than [BaLS]. We also wish to explain a possible confusion with respect to the order of parts and spelling of Chinese names. We put them without any abbreviations, often with the last name written first as is customary in original. Sometimes this is different from the citations in other sources. One can obtain all variations of writing any specific name by consulting the authors database of Mathematical Reviews a

Path-kipas Ramsey numbers

For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers $R(P_n,\hat{K}_m)$, where $P_n$ is a path on $n$ vertices and $\hat{K}_m$ is the graph obtained from the join of $K_1$ and $P_m$. We determine the exact values of $R(P_n,\hat{K}_m)$ for the following values of $n$ and $m$: $1\le n \le 5$ and $m\ge 3$; $n\ge 6$ and ($m$ is odd, $3\le m\le 2n-1$) or ($m$ is even, $4\le m \le n+1$); $6\le n\le 7$ and $m=2n-2$ or $m \ge 2n$; $n\ge 8$ and $m=2n-2$ or $m=2n$ or ($q\cdot n-2q+1 \le m\le q\cdot n-q+2$ with $3\le q\le n-5$) or $m\ge (n-3)^2$; odd $n\ge 9$ and ($q\cdot n-3q+1\le m\le q\cdot n-2q$ with $3\le q\le (n-3)/2$) or ($q\cdot n-q-n+4m\le q\cdot n-2q$ with $(n-1)/2\le q\le n-4).$ Moreover, we give lower bounds and upper bounds for $R(P_n ,\hat{K}_m)$ for the other values of $m$ and $n$

The Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths

The Ramsey number $R(G, H)$ for a pair of graphs $G$ and $H$ is defined as the smallest integer $n$ such that, for any graph $F$ on $n$ vertices, either $F$ contains $G$ or $\overline{F}$ contains $H$ as a subgraph, where $\overline{F}$ denotes the complement of $F$. We study Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths and determine these numbers for some cases. We extend many known results studied in [5, 14, 18, 19, 20]. In particular we count the numbers $R(K_1+L_n, P_m)$ and $R(K_1+L_n, C_m)$ for some integers $m$, $n$, where $L_n$ is a linear forest of order $n$ with at least one edge

Ramsey Goodness and Beyond

In a seminal paper from 1983, Burr and Erdos started the systematic study of Ramsey numbers of cliques vs. large sparse graphs, raising a number of problems. In this paper we develop a new approach to such Ramsey problems using a mix of the Szemeredi regularity lemma, embedding of sparse graphs, Turan type stability, and other structural results. We give exact Ramsey numbers for various classes of graphs, solving all but one of the Burr-Erdos problems.Comment: A new reference is adde

Advances in Discrete Applied Mathematics and Graph Theory

The present reprint contains twelve papers published in the Special Issue “Advances in Discrete Applied Mathematics and Graph Theory, 2021” of the MDPI Mathematics journal, which cover a wide range of topics connected to the theory and applications of Graph Theory and Discrete Applied Mathematics. The focus of the majority of papers is on recent advances in graph theory and applications in chemical graph theory. In particular, the topics studied include bipartite and multipartite Ramsey numbers, graph coloring and chromatic numbers, several varieties of domination (Double Roman, Quasi-Total Roman, Total 3-Roman) and two graph indices of interest in chemical graph theory (Sombor index, generalized ABC index), as well as hyperspaces of graphs and local inclusive distance vertex irregular graphs