On pancyclic line graphs
On partial cubes and graphs with convex intervals
A graph is called a partial cube if it admits an isometric embedding into a hypercube. Subdivisions of wheels are considered with respect to such embeddings and with respect to the convexity of their intervals. This allows us to answer in negative a question of Chepoi and Tardif from 1994 whether all bipartite graphs with convex intervals are partial cubes. On a positive side we prove that a graph which is bipartite, has convex intervals, and is not a partial cube, always contains a subdivision...
On Partially Directed Eulerian Multigraphs
On partially directed geodetic graphs
On partially directed -graphs
On partition graphs and generalizations of line graphs
On partitionable, confidentially connected and unbreakable graphs.
On partitions and cyclotomic polynomials.
On partitions avoiding 3-crossings.
On partitions of hereditary properties of graphs
In this paper a concept 𝓠-Ramsey Class of graphs is introduced, where 𝓠 is a class of bipartite graphs. It is a generalization of well-known concept of Ramsey Class of graphs. Some 𝓠-Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that 𝓣₂, the class of all outerplanar graphs, is not 𝓓₁-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property 𝓟 . For 𝓣₂ we found two bounds (Theorem 4). An improvement, in some sense,...
On partitions, surjections, and Stirling numbers.
On partitions with difference conditions.
On partitions with limited summands
On Path-Pairability in the Cartesian Product of Graphs
We study the inheritance of path-pairability in the Cartesian product of graphs and prove additive and multiplicative inheritance patterns of path-pairability, depending on the number of vertices in the Cartesian product. We present path-pairable graph families that improve the known upper bound on the minimal maximum degree of a path-pairable graph. Further results and open questions about path-pairability are also presented.
On path-quasar Ramsey numbers
Let G1 and G2 be two given graphs. The Ramsey number R(G1,G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or Ḡ contains a G2. Parsons gave a recursive formula to determine the values of R(Pn,K1,m), where Pn is a path on n vertices and K1,m is a star on m+1 vertices. In this note, we study the Ramsey numbers R(Pn,K1,m), where Pn is a linear forest on m vertices. We determine the exact values of R(Pn,K1∨Fm) for the cases m ≤ n and m ≥ 2n, and for the case...
On pattern-avoiding partitions.
On pebbling graphs by their blocks.
On pendant vertices in random graphs
On percolation in random graphs with given vertex degrees.
On perfect and unique maximum independent sets in graphs
A perfect independent set of a graph is defined to be an independent set with the property that any vertex not in has at least two neighbors in . For a nonnegative integer , a subset of the vertex set of a graph is said to be -independent, if is independent and every independent subset of with is a subset of . A set of vertices of is a super -independent set of if is -independent in the graph , where is the bipartite graph obtained from by deleting all edges...