This article surveys results on maximal k-degenerate graphs, k-trees, and related classes
including simple k-trees, k-paths, maximal outerplanar graphs, and Apollonian networks …

A proper vertex coloring φ of graph G is said to be odd if for each non-isolated vertex x∈ V
(G) there exists a color c such that φ− 1 (c)∩ N (x) is odd-sized. The minimum number of …

We consider $2 $-colourings $ f: E (G)\rightarrow\{-1, 1\} $ of the edges of a graph $ G $ with
colours $-1$ and $1 $ in $\mathbb {Z} $. A subgraph $ H $ of $ G $ is said to be a zero-sum …

Let $ G $ be a simple graph of order $ n $ with degree sequence $(d_1, d_2,\cdots, d_n) $.
For an integer $ p> 1$, let $ e_p (G)=\sum_ {i= 1}^ nd^{p} _i $ and let $ ex_p (n, H) $ be the …

The k-core of a graph is the maximal subgraph with minimum degree at least k. It is easily
shown that this subgraph is unique, the cores of a graph are nested, and that it can be found …

Let G be a connected graph. A cyclic base ordering of G is a cyclic ordering of elements in E
(G) such that every cyclically consecutive| V (G)|− 1 edges form a spanning tree of G. The …

A graph is k-degenerate if its vertices can be successively deleted so that when deleted,
each has degree at most k. These graphs were introduced by Lick and White in 1970 and …

A graph is k-degenerate if its vertices can be successively deleted so that when deleted,
they have degree at most k. A k-tree is a graph that can be formed by starting with Kk+ 1 and …

A k-monocore graph is a graph which has its minimum degree and degeneracy both equal
to k. Integer sequences that can be the degree sequence of some k-monocore graph are …