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11 papers · 2 filters
A Proof of a Conjecture of Ohba
Jonathan A. Noel, Bruce A. Reed, Hehui Wu
We prove a conjecture of Ohba which says that every graph on at most vertices satisfies .
Integral Cayley multigraphs over Abelian and Hamiltonian groups
Matt DeVos, Roi Krakovski, Bojan Mohar +1
It is shown that a Cayley multigraph over a group with generating multiset is integral (i.e., all of its eigenvalues are integers) if lies in the integral cone over the…
On additive complexity of infinite words
Graham Banero
We consider questions related to the structure of infinite words (over an integer alphabet) with bounded additive complexity, i.e., words with the property that the number of disti…
Strongly even-cycle decomposable graphs
Tony Huynh, Andrew D. King, Sang-il Oum +1
A graph is strongly even-cycle decomposable if the edge set of every subdivision with an even number of edges can be partitioned into cycles of even length. We prove that several f…
Properties of the corolla polynomial of a 3-regular graph
Dirk Kreimer, Karen Yeats
We investigate combinatorial properties of a graph polynomial indexed by half-edges of a graph which was introduced recently to understand the connection between Feynman rules for…
A note on forbidding clique immersions
Matt DeVos, Jessica McDonald, Bojan Mohar +1
Robertson and Seymour proved that the relation of graph immersion is well-quasi-ordered for finite graphs. Their proof uses the results of graph minors theory. Surprisingly, there…