Related papers: n-Arc Connected Spaces
It is shown that a.a.s. as soon as a Kronecker graph becomes connected its diameter is bounded by a constant.
In this paper, we characterize graphs with circular chromatic number less than 3 in terms of certain balancing labellings studied in the context of signed graphs. In fact, we construct a signed graph which is universal for all such…
Associative spectra of graph algebras are examined with the help of homomorphisms of DFS trees. Undirected graphs are classified according to the associative spectra of their graph algebras; there are only three distinct possibilities:…
Word-representable graphs, characterized by the existence of a semi-transitive orientation, form a well-studied class of graphs. Comparability graphs form another well-studied class and constitute a subclass of word-representable graphs.…
A graph is called equimatchable if all of its maximal matchings have the same size. Frendrup et al. [8] provided a characterization of equimatchable graphs with girth at least $5$. In this paper, we extend this result by providing a…
In the following text we show if $X$ is an Alexandroff space, then $f:X\to Y$ has closed graph if and only if it has constant closed value on each connected component of $X$. Moreover, if $X$ an Alexandroff space and $f:X\to Y$ has closed…
This paper shows that, for any integers $n$ and $k$ with $0\leqslant k \leqslant n-2$, at least $(k+1)!(n-k-1)$ vertices or edges have to be removed from an $n$-dimensional star graph to make it disconnected and no vertices of degree less…
For a given graph consider a pair of disjoint matchings the union of which contains as many edges as possible. Furthermore, consider the relation of the cardinalities of a maximum matching and the largest matching in those pairs. It is…
A non-planar graph is almost-planar if either deleting or contracting any edge makes it planar. A graph with $n$ vertices is pancyclic if it contains a cycle of every length from $3$ to $n$, and it is Hamiltonian if it contains a cycle of…
Let S denote the family of all subspaces of the plane that are graphs of functions from the real line R to itself. We prove that S has two subfamilies G,H of spaces such that the cardinality of G is c (the cardinality of the continuum) and…
A graph is called a $k$-planar unit distance graph if it can be drawn in the plane such that every edge is a unit line segment and is involved in at most $k$ crossings. We investigate $u_k(n)$, the maximum number of edges of such graphs on…
Sufficient conditions are given for the computation of accessing arcs and arcs that links boundary components of multiply connected domains. The existence of a not-computably-accessible but computable point on a computably compact arc is…
Recently, Ali et al. posed several open problems concerning extremal graphs with respect to the ABS index. These problems involve characterizing graphs that attain the maximum ABS index within specific graph classes, including: connected…
We establish tight lower and upper bounds on the number of edges in traceable graphs in several classes of dense graphs. A graph is traceable if it has a Hamiltonian path. We show that the bound is: - quadratic for the class of graphs of…
A signed graph has edge weights drawn from the set $\{+1,-1\}$, and is termed sign-balanced if it is equivalent to an unsigned graph under the operation of sign switching; otherwise it is called sign-unbalanced. A nut graph has a one…
Two previous papers, arXiv:1803.00284 and arXiv:1803.00281, introduced and studied strong subgraph $k$-connectivity of digraphs obtaining characterizations, lower and upper bounds and computational complexity results for the new digraph…
A graph is c-closed if every pair of vertices with at least c common neighbors is adjacent. The c-closure of a graph G is the smallest number such that G is c-closed. Fox et al. [ICALP '18] defined c-closure and investigated it in the…
We introduce a new arc in directed graphs of integers. Among other things, we determine the positive integers that have arcs to all except a finite number of positive integers. We also propose some possible research problems at the end of…
A circular arc graph is the intersection graph of a collection of connected arcs on the circle. We solve a Tur'an-type problem for circular arc graphs: for n arcs, if m and M are the minimum and maximum number of arcs that contain a common…
A connected graph is 4-connected if it contains at least five vertices and removing any three of them does not disconnect it. A frequent preprocessing step in graph drawing is to decompose a plane graph into its 4-connected components and…