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- https://math.libretexts.org/Courses/Saint_Mary's_College_Notre_Dame_IN/SMC%3A_MATH_339_-_Discrete_Mathematics_(Rohatgi)/Text/5%3A_Graph_Theory/5.5%3A_Euler_Paths_and_CircuitsAn Euler path, in a graph or multigraph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Our goal is to fin...An Euler path, in a graph or multigraph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Our goal is to find a quick way to check whether a graph (or multigraph) has an Euler path or circuit.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_300%3A_Mathematical_Ideas_Textbook_(Muranaka)/06%3A_Miscellaneous_Extra_Topics/6.04%3A_Graph_Theory/6.4.02%3A_Euler_CircuitsLeonhard Euler first discussed and used Euler paths and circuits in 1736. Rather than finding a minimum spanning tree that visits every vertex of a graph, an Euler path or circuit can be used to find ...Leonhard Euler first discussed and used Euler paths and circuits in 1736. Rather than finding a minimum spanning tree that visits every vertex of a graph, an Euler path or circuit can be used to find a way to visit every edge of a graph once and only once. This would be useful for checking parking meters along the streets of a city, patrolling the streets of a city, or delivering mail.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Book%3A_College_Mathematics_for_Everyday_Life_(Inigo_et_al)/06%3A_Graph_Theory/6.03%3A_Euler_CircuitsLeonhard Euler first discussed and used Euler paths and circuits in 1736. Rather than finding a minimum spanning tree that visits every vertex of a graph, an Euler path or circuit can be used to find ...Leonhard Euler first discussed and used Euler paths and circuits in 1736. Rather than finding a minimum spanning tree that visits every vertex of a graph, an Euler path or circuit can be used to find a way to visit every edge of a graph once and only once. This would be useful for checking parking meters along the streets of a city, patrolling the streets of a city, or delivering mail.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/10%3A_Graph_Theory/10.05%3A_Euler_Paths_and_CircuitsAn Euler path, in a graph or multigraph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Our goal is to fin...An Euler path, in a graph or multigraph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Our goal is to find a quick way to check whether a graph (or multigraph) has an Euler path or circuit.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_and_Graph_Theory_(Guichard)/05%3A_Graph_Theory/5.02%3A_Euler_Circuits_and_WalksThe Euler circuits of the graphs \(G_i\) are \[\eqalign{ &w_{1,1},w_{1,2},\ldots,w_{1,m_1}=w_{1,1}\cr &w_{2,1},w_{2,2},\ldots,w_{2,m_2}=w_{2,1}\cr &\vdots\cr &w_{k,1},w_{k,2},\ldots,w_{k,m_k}=w_{k,1}....The Euler circuits of the graphs \(G_i\) are \[\eqalign{ &w_{1,1},w_{1,2},\ldots,w_{1,m_1}=w_{1,1}\cr &w_{2,1},w_{2,2},\ldots,w_{2,m_2}=w_{2,1}\cr &\vdots\cr &w_{k,1},w_{k,2},\ldots,w_{k,m_k}=w_{k,1}.\cr }\nonumber\] By pasting together the original closed walk with these, we form a closed walk in \(G\) that uses every edge exactly once: \[\eqalign{ v_0,v_1,&\ldots,v_{i_1}=w_{1,1},w_{1,2},\ldots,w_{1,m_1}=v_{i_1},v_{i_1+1},\cr &\ldots, v_{i_2}=w_{2,1},\ldots,w_{2,m_2}=v_{i_2},v_{i_2+1},\cr &\ld…
- https://math.libretexts.org/Courses/Florida_SouthWestern_State_College/MGF_1131%3A_Mathematics_in_Context__(FSW)/07%3A_Graph_Theory/7.02%3A_Euler_Circuits_and_Eulerization_of_GraphThis section covers Euler paths and circuits, key concepts in graph theory from the Konigsberg Bridge Problem. An Euler path visits every edge once with distinct starting and ending vertices, while an...This section covers Euler paths and circuits, key concepts in graph theory from the Konigsberg Bridge Problem. An Euler path visits every edge once with distinct starting and ending vertices, while an Euler circuit starts and ends at the same vertex. A graph can have these if it meets specific vertex degree conditions.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_(Levin)/4%3A_Graph_Theory/4.4%3A_Euler_Paths_and_CircuitsAn Euler path, in a graph or multigraph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Our goal is to fin...An Euler path, in a graph or multigraph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Our goal is to find a quick way to check whether a graph (or multigraph) has an Euler path or circuit.
