Generalized Ramsey theory and decomposable properties of graphs

Constructing vertex decomposable graphs

‎Recently‎, ‎some techniques such as adding whiskers and attaching graphs to vertices of a given graph‎, ‎have been proposed for constructing a new vertex decomposable graph‎. ‎In this paper‎, ‎we present a new method for constructing vertex decomposable graphs‎. ‎Then we use this construction to generalize the result due to Cook and Nagel‎.

Vertex Decomposable Simplicial Complexes Associated to Path Graphs

Introduction Vertex decomposability of a simplicial complex is a combinatorial topological concept which is related to the algebraic properties of the Stanley-Reisner ring of the simplicial complex. This notion was first defined by Provan and Billera in 1980 for k-decomposable pure complexes which is known as vertex decomposable when . Later Bjorner and Wachs extended this concept to non-pure ...

Some Algebraic and Combinatorial Properties of the Complete $T$-Partite Graphs

In this paper, we characterize the shellable complete $t$-partite graphs. We also show for these types of graphs the concepts vertex decomposable, shellable and sequentially Cohen-Macaulay are equivalent. Furthermore, we give a combinatorial condition for the Cohen-Macaulay complete $t$-partite graphs.

Distinct edge geodetic decomposition in graphs

Let G=(V,E) be a simple connected graph of order p and size q. A decomposition of a graph G is a collection π of edge-disjoint subgraphs G_1,G_2,…,G_n of G such that every edge of G belongs to exactly one G_i,(1≤i ≤n). The decomposition 〖π={G〗_1,G_2,…,G_n} of a connected graph G is said to be a distinct edge geodetic decomposition if g_1 (G_i )≠g_1 (G_j ),(1≤i≠j≤n). The maximum cardinality of π...

Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs