1. CMB Online first
 Alfuraidan, Monther Rashed

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph
We study the existence of fixed points for contraction multivalued
mappings in modular metric spaces endowed with a graph. The
notion of a modular metric on an arbitrary set and the corresponding
modular spaces, generalizing classical modulars over linear spaces
like Orlicz spaces, were recently introduced. This paper can
be seen as a generalization of Nadler's and Edelstein's fixed
point theorems to modular metric spaces endowed with a graph.
Keywords:fixed point theory, modular metric spaces, multivalued contraction mapping, connected digraph. Categories:47H09, 46B20, 47H10, 47E10 

2. CMB 2013 (vol 57 pp. 141)
 Mukwembi, Simon

Size, Order, and Connected Domination
We give a sharp upper bound on the size of a
trianglefree graph of a given order and connected domination. Our
bound, apart from
strengthening an old classical theorem of Mantel and of
TurÃ¡n , improves on a theorem of Sanchis.
Further, as corollaries, we settle a long standing
conjecture of Graffiti on the leaf number and local independence for
trianglefree graphs and answer a question of Griggs, Kleitman and
Shastri on a lower bound of the leaf number in
trianglefree graphs.
Keywords:size, connected domination, local independence number, leaf number Category:05C69 

3. CMB 2012 (vol 56 pp. 860)
 van Mill, Jan

On Countable Dense and $n$homogeneity
We prove that a connected, countable dense homogeneous space is
$n$homogeneous for every $n$, and strongly 2homogeneous provided it
is locally connected. We also present an example of a connected and
countable dense homogeneous space which is not strongly
2homogeneous. This answers Problem 136 of Watson in the Open Problems
in Topology Book in the negative.
Keywords:countable dense homogeneous, connected, $n$homogeneous, strongly $n$homogeneous, counterexample Categories:54H15, 54C10, 54F05 

4. CMB 2011 (vol 54 pp. 244)
 Daniel, D. ; Nikiel, J.; Treybig, L. B.; Tuncali, H. M.; Tymchatyn, E. D.

Homogeneous Suslinian Continua
A continuum is said to be Suslinian if it does not
contain uncountably many
mutually exclusive nondegenerate subcontinua. Fitzpatrick and
Lelek have shown that a metric Suslinian continuum $X$ has the
property that the set of points at which $X$ is connected im
kleinen is dense in $X$. We extend their result to Hausdorff Suslinian continua
and obtain a number of corollaries. In particular, we prove that a homogeneous,
nondegenerate, Suslinian continuum is a simple closed curve and that each separable,
nondegenerate, homogenous, Suslinian continuum is metrizable.
Keywords:connected im kleinen, homogeneity, Suslinian, locally connected continuum Categories:54F15, 54C05, 54F05, 54F50 

5. CMB 2009 (vol 52 pp. 416)
 Malik, Shabnam; Qureshi, Ahmad Mahmood; Zamfirescu, Tudor

Hamiltonian Properties of Generalized Halin Graphs
A Halin graph is a graph $H=T\cup C$, where $T$ is a tree with no
vertex of degree two, and $C$ is a cycle connecting the endvertices
of $T$ in the cyclic order determined by a plane embedding of $T$.
In this paper, we define classes of generalized Halin graphs, called
$k$Halin graphs, and investigate their Hamiltonian properties.
Keywords:$k$Halin graph, Hamiltonian, Hamiltonian connected, traceable Categories:05C45, 05C38 

6. CMB 2005 (vol 48 pp. 195)
 Daniel, D.; Nikiel, J.; Treybig, L. B.; Tuncali, H. M.; Tymchatyn, E. D.

On Suslinian Continua
A continuum is said to be Suslinian if it does not contain uncountably
many mutually exclusive nondegenerate subcontinua. We prove that
Suslinian continua are perfectly normal and rimmetrizable. Locally
connected Suslinian continua have weight at most $\omega_1$ and under
appropriate settheoretic conditions are metrizable. Nonseparable
locally connected Suslinian continua are rimfinite on some open set.
Keywords:Suslinian continuum, Souslin line, locally connected, rimmetrizable,, perfectly normal, rimfinite Categories:54F15, 54D15, 54F50 
