On a Conjecture Concerning the Petersen Graph
نویسندگان
چکیده
منابع مشابه
On a Conjecture Concerning the Petersen Graph
Robertson has conjectured that the only 3-connected, internally 4-connected graph of girth 5 in which every odd cycle of length greater than 5 has a chord is the Petersen graph. We prove this conjecture in the special case where the graphs involved are also cubic. Moreover, this proof does not require the internal-4-connectivity assumption. An example is then presented to show that the assumpti...
متن کاملOn a Conjecture Concerning the Petersen Graph: Part II
Robertson conjectured that the only 3-connected, internally 4-connected graph of girth 5 in which every odd cycle of length greater than 5 has a chord is the Petersen graph. We provide a counterexample to this conjecture.
متن کاملOn a conjecture concerning the orientation number of a graph
For a connected graph G containing no bridges, let D(G) be the family of strong orientations of G; and for any D ∈ D(G), we denote by d(D) the diameter of D. The orientation number −→ d (G) of G is defined by −→ d (G) = min{d(D)|D ∈ D(G)}. Let G(p, q;m) denote the family of simple graphs obtained from the disjoint union of two complete graphs K p and Kq by adding m edges linking them in an arbi...
متن کاملHadwiger Conjecture for Inflations of the Petersen Graph
LATEX by Adam Jobson For a family of graphs F closed under subgraphs, and a graph G from F , define a game (G,F) played by Builder and Painter. The game begins with Builder presenting an edge and Painter coloring the edge red or blue. On each turn thereafter, Builder adds another edge to the red-blue colored graph present (adding vertices if needed), so that the new graph, viewed uncolored, is ...
متن کاملAddressing the Petersen graph
Motivated by a problem on message routing in communication networks, Graham and Pollak proposed a scheme for addressing the vertices of a graph G by N -tuples of three symbols in such a way that distances between vertices may readily be determined from their addresses. They observed that N ≥ h(D), the maximum of the number of positive and the number of negative eigenvalues of the distance matri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/507