Minimum degree, leaf number and traceability

Minimum degree algorithms for stability number

Girth, minimum degree, independence, and broadcast independence

An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...

Chromatic number and minimum degree of Kr+1-free graphs

Let (G) be the minimum degree of a graph G: A number of results about trianglefree graphs determine the maximum chromatic number of graphs of order n with (G) n=3: In this paper these results are extended to Kr+1-free graphs of order n with (G) (1 2= (2r 1))n: In particular: (a) there exist Kr+1-free graphs of order n with (G) > (1 2= (2r 1))n o (n) and arbitrary large chromatic number; (b) if ...

On Independent Domination Number of Graphs with given Minimum Degree

We prove a new upper bound on the independent domination number of graphs in terms of the number of vertices and the minimum degree. This bound is slightly better than that by J. Haviland 3] and settles Case = 2 of the corresponding conjecture by O. Favaron 2].

The Total Chromatic Number of Graphs of High Minimum Degree

If G is a simple graph with minimum degree <5(G) satisfying <5(G) ^ f(| K(C?)| -f-1) the total chromatic number conjecture holds; moreover if S(G) ^ f| V(G)\ then #T(G) < A(G) + 3. Also if G has odd order and is regular with d{G) ^ \^/1\V{G)\ then a necessary and sufficient condition for ^T((7) = A((7)+ 1 is given.