: We present an improved upper bound of O(d1+ 1 m−1 ) for the (2, F)-subgraph chromatic number χ2,F (G) of any graph G of maximum degree d. Here, m denotes the minimum number of...
Researchers have proposed a variety of metrics to measure important graph properties, for instance, in social, biological, and computer networks. Values for a particular graph met...
Priya Mahadevan, Dmitri V. Krioukov, Kevin R. Fall...
d Abstract) Noga Alon1, , Michael Capalbo2, , Yoshiharu Kohayakawa3, , Vojtˇech R¨odl4,† , Andrzej Ruci´nski5,‡ , and Endre Szemer´edi6,§ 1 Department of Mathematics, Raym...
Noga Alon, Michael R. Capalbo, Yoshiharu Kohayakaw...
We show that any face hitting set of size n of a connected planar graph with a minimum degree of at least 3 is contained in a connected subgraph of size 5n − 6. Furthermore we s...
We introduce a generic approach for counting subgraphs in a graph. The main idea is to relate counting subgraphs to counting graph homomorphisms. This approach provides new algori...